| Preface |
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v | |
| Acknowledgements |
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vii | |
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xv | |
| Commentary on Burnside's Life and Work |
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1 | (2) |
| Foreword |
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3 | (4) |
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| Bibliography of William Burnside |
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7 | (8) |
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The context of Burnside's contributions to group theory |
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15 | (24) |
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A still unsettled question |
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39 | (6) |
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Burnside and finite simple groups |
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45 | (10) |
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Burnside's research on representation theory |
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55 | (8) |
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Burnside's applied mathematics |
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63 | (8) |
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`William Burnside', reprinted from the Journal of the London Mathematical Society, Vol. 3 (1928) |
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71 | (18) |
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89 | (22) |
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111 | (678) |
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[1883a] The elliptic functions of 1/3K, &c. |
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113 | (4) |
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[1883b] Note on centre of pressure of a plane polygon |
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117 | (2) |
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[1884a] On certain spherical harmonics |
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119 | (6) |
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[1887a] On the trisection of the periods for Weierstrass's elliptic functions |
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125 | (4) |
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[1887b] On the partition of energy between the translatory and rotational motions of a set of non-homogeneous elastic spheres |
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129 | (8) |
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[1888a] On a simplified proof of Maxwell's theorem |
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137 | (4) |
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[1888b] Note on the potential of an elliptic cylinder |
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141 | (6) |
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[1888c] On deep-water waves resulting from a limited original disturbance |
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147 | (16) |
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[1889a] On the small wave-motions of a heterogeneous fluid under gravity |
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163 | (6) |
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[1889b] Mathematical notes 1: Geometrical interpretation of a condition of integrability |
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169 | (2) |
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[1889c] Mathematical notes 2: Propagation of energy in the electro-magnetic field |
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171 | (2) |
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[1889d] The lines of zero length on a surface as curvilinear coordinates |
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173 | (6) |
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[1889e] On the resultant of two finite displacements of a rigid body |
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179 | (6) |
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[1890a] On the differential equation of confocal sphero-conics |
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185 | (4) |
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[1890b] On the surfaces whose lines of curvature are all plane |
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189 | (8) |
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[1890c] On a property of plane isothermal curves |
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197 | (6) |
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[1890d] Note on a paper relating to the theory of functions |
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203 | (4) |
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[1891a] On a case of streaming motion |
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207 | (2) |
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[1891b] Note on the addition theorem for hyperbolic functions |
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209 | (4) |
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[1891c] On a property of linear substitutions |
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213 | (4) |
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[1891d] On functions determined from their discontinuities, and a certain form of boundary condition |
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217 | (14) |
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[1891e] On a certain Riemann's surface |
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231 | (8) |
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[1891f] On the form of closed curves of the third class |
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239 | (2) |
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[1891g] Algebraical notes. I: On the Jacobian of two quadratics. II: On a system of simultaneous equations |
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241 | (4) |
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[1891h] Two notes on Weierstrass's P(u). 1: Forms of the addition equation. 2: On P(u) considered as a covariant of a quartic |
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245 | (4) |
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[1891k] On a class of automorphic functions |
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249 | (40) |
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[1892a] On the form of hyperelliptic integrals of the first order, which are expressible as the sum of two elliptic integrals |
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289 | (14) |
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[1892b] On the application of Abel's theorem to elliptic integrals of the first kind |
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303 | (8) |
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[1892c] On the linear transformation of the elliptic differential |
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311 | (8) |
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[1892d] Prof. Burnside's paper on the partition of energy, R.S.E., July 1887 |
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319 | (2) |
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[1892e] Further note on automorphic functions |
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321 | (16) |
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[1892f] Note on pseudo-elliptic integrals |
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337 | (8) |
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[1892g] On the division of the periods of elliptic functions by 9 |
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345 | (8) |
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[1892h] Note on the equation y2 = x(x4 -- 1) |
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353 | (4) |
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[1893a] On a problem of conformal representation |
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357 | (20) |
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[1893b] Note on linear substitutions |
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377 | (4) |
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[1893c] On the finite displacement of a rigid body |
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381 | (4) |
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[1893d] Note on functions of a real variable |
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385 | (4) |
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[1893e] Note on the theory of groups |
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389 | (8) |
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[1893f] On the curve of intersection of two quadrics |
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397 | (4) |
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[1893g] Notes on the theory of groups of finite order. I: On the proof of Sylow's Theorem. II: On the possibility of simple groups whose orders are the products of four primes |
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401 | (10) |
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[1893h] On a property of certain determinants |
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411 | (4) |
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[1894a] On Green's function for a system of non-intersecting spheres |
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415 | (8) |
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[1894b] On an application of the theory of groups to Kirkman's problem |
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423 | (8) |
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[1894c] On a class of groups defined by congruences |
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431 | (28) |
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[1894d] On a system of linear congruences |
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459 | (8) |
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[1894e] On certain composite groups |
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467 | (16) |
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[1894f] On the kinematics of non-Euclidean space |
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483 | (24) |
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[1894g] Note on ternary substitutions of determinant unity with integral coefficients |
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507 | (4) |
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[1894h] On a class of groups defined by congruences (second paper) |
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511 | (50) |
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[1895a] Notes on the theory of groups of finite order (Notes III-VII) |
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561 | (26) |
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[1895b] Correction to a former paper [1893e] |
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587 | (2) |
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[1895c] Notes on the theory of groups of finite order (continued) (Notes VIII, IX) |
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589 | (14) |
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[1895d] On two theorems in elementary kinematics |
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603 | (4) |
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[1896a] On doubly-transitive groups of degree n and order n(n -- 1) |
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607 | (8) |
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[1896b] On the isomorphism of a group with itself |
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615 | (14) |
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[1896c] On doubly-transitive groups of degree 2m and order 2m (2m -- 1) |
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629 | (4) |
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[1896d] Note on the symmetric group |
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633 | (12) |
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[1897b] The construction of the straight line joining two given points |
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645 | (8) |
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[1898a1] On the continuous group that is defined by any given group of finite order |
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653 | (18) |
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[1898a2] On the continuous group that is defined by any given group of finite order (second paper) |
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671 | (22) |
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[1898b] On plane equipotential surfaces |
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693 | (10) |
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[1898c] On linear homogeneous continuous groups whose operations are permutable |
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703 | (28) |
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[1898d] Note on the simple group of order 504 |
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731 | (4) |
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[1898e] The trigonometry of a rectangular gauche hexagon |
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735 | (6) |
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[1898f] On the representation of a group of finite order as a substitution group |
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741 | (2) |
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[1898g] On the canonical form of a linear substitution of finite order |
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743 | (4) |
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[1898h] Correction to the paper on the representation of a group of finite order as a substitution group [1898f] |
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747 | (2) |
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[1898k] Appendix to `The geodesic geometry of surfaces in non-Euclidean space' |
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749 | (4) |
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[1899a] On the reduction of a linear substitution to its canonical form |
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753 | (16) |
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[1899b] Sketch of the late Prof. Sophus Lie's mathematical work |
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769 | (4) |
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[1899c1] Review of Introduction to the Theory of Analytic Functions |
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773 | (6) |
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[1899c2] Discussion on Theory of Functions (untitled letter) |
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779 | (2) |
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[1899d] On a class of groups of finite order |
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781 | (8) |
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789 | (794) |
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[1900a] On transitive groups of degree n and class n -- 1 |
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791 | (8) |
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[1900b] On group-characteristics |
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799 | (18) |
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[1900c1] On some properties of groups of odd order |
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817 | (24) |
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[1900c2] On some properties of groups of odd order (second paper) |
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841 | (12) |
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[1900d] On cyclotomic trisection |
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853 | (2) |
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[1901a] Note on the symmetric group |
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855 | (6) |
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[1901b] On the composition of group characteristics |
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861 | (8) |
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[1901c] On the general projective transformation |
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869 | (4) |
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[1901d] Two notes on the projective invariants of systems of points |
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873 | (10) |
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[1901e] On groups which contain 1 + 2p or 1 + 4p subgroups of order pα |
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883 | (6) |
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[1901f] On the representation of a group of finite order as a permutation group, and on the composition of permutation groups |
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889 | (10) |
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[1901g] On the lines of curvature of inverse surfaces |
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899 | (2) |
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[1901h] On the characteristic equations of certain linear substitutions |
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901 | (6) |
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[1902a] On the roots of the Hessian of a binary quartic |
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907 | (6) |
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[1902b] On groups in which every two conjugate operations are permutable |
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913 | (10) |
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[1902c] On an unsettled question in the theory of discontinuous groups |
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923 | (10) |
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[1902d] On soluble groups of linear substitutions |
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933 | (4) |
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[1902e] On the four rotations which displace one orthogonal system of axes into another |
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937 | (6) |
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[1902f] On groups which are linear and homogeneous in both variables and parameters |
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943 | (16) |
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[1902g] Theory of groups (Encyclopaedia article) |
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959 | (80) |
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[1903a] On soluble irreducible groups of linear substitutions in a prime number of variables |
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1039 | (8) |
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[1903b] On an arithmetical theorem connected with roots of unity, and its application to group characteristics |
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1047 | (6) |
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[1903c] On composite inversion and allied transformations |
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1053 | (14) |
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[1903d] On the representation of a group of finite order as an irreducible group of linear substitutions and the direct establishment of the relations between the group-characteristics |
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1067 | (8) |
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[1903e] On reciprocal linear homogeneous groups |
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1075 | (4) |
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[1903f] On groups which admit certain isomorphisms |
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1079 | (4) |
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[1903g] On the coordinates of the eighth point common to a system of quadrics through seven given points |
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1083 | (2) |
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[1904a] On groups of order pα qβ |
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1085 | (6) |
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[1904b] On linear substitutions of determinant unity with integral coefficients |
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1091 | (6) |
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[1904c] On the reduction of a group of homogeneous linear substitutions of finite order |
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1097 | (20) |
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[1904d] On groups of order pα qβ (second paper) |
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1117 | (6) |
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[1905a] On the complete reduction of any transitive permutation-group; and on the arithmetical nature of the coefficients in its irreducible components |
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1123 | (14) |
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[1905b] On the condition of reducibility of any group of linear substitutions |
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1137 | (6) |
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[1905c] On criteria for the finiteness of the order of a group of linear substitutions |
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1143 | (6) |
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[1905d] On finite groups in which all the Sylow subgroups are cyclical |
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1149 | (6) |
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[1905e] On a general property of finite irreducible groups of linear substitutions |
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1155 | (6) |
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[1905f] On the arithmetical nature of the coefficients in a group of linear substitutions of finite order (second paper) |
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1161 | (10) |
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[1905g] On the Hessian configuration and its connection with the group of 360 plane collineations |
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1171 | (18) |
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[1906a] On the simple group of order 25920 |
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1189 | (30) |
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[1906b] On the figure consisting of a regular pentagon and the line at infinity |
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1219 | (4) |
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[1906c] On simply transitive groups of prime degree |
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1223 | (8) |
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[1908a] The alternating functions of three and of four variables |
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1231 | (2) |
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[1908b] An approximate quadrature formula |
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1233 | (2) |
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[1908c] On the theory of groups of finite order (Presidential address) |
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1235 | (8) |
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[1908d] On the arithmetical nature of the coefficients in a group of linear substitutions (third paper) |
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1243 | (6) |
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[1908e] Review of An Introduction to the Theory of Groups of Finite Order |
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1249 | (2) |
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[1909a] On a configuration of twenty-seven hyper-planes in four-dimensional space |
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1251 | (6) |
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[1909b] On the group of the twenty-seven lines of a cubic surface |
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1257 | (6) |
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[1910a] On the representation of a group of finite order as a group of linear substitutions with rational coefficients |
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1263 | (10) |
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1273 | (4) |
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[1910c] On the coefficients in groups of linear substitutions of finite order |
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1277 | (2) |
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[1910d] The most general metabelian group of finite order with two generators |
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1279 | (4) |
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[1910e] Theory of groups (Encyclopaedia article) |
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1283 | (36) |
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[1911b] The determination of all groups of rational linear substitutions of finite order which contain the symmetric group in the variables |
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1319 | (26) |
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[1911c] The condition that an irreducible group of linear substitutions on n variables of finite order may contain a substitution with n -- 1 unit multipliers |
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1345 | (4) |
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[1911d] On the outer isomorphisms of a group |
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1349 | (4) |
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[1911e] On the double-six which admits a group of 120 collineations into itself |
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1353 | (4) |
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[1912a] On some properties of groups whose orders are powers of primes |
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1357 | (22) |
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[1912b] On groups of linear substitutions of finite order which possess quadratic invariants |
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1379 | (6) |
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[1913a] On some properties of groups whose orders are powers of primes (second paper) |
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1385 | (8) |
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[1914a] On the rational solutions of the equation X3 + Y3 + Z3 = 0 in quadratic fields |
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1393 | (4) |
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[1914b] On the rational determination of a plane quartic from seven given bitangents |
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1397 | (4) |
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[1914c] An elementary proof of a property of groups of finite order |
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1401 | (6) |
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[1914d] On a configuration of 21 points and 21 lines which arises from the complete quadrilateral and determines the group of 168 plane collineations |
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1407 | (6) |
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[1914e] On the modification of a train of waves as it advances into shallow water |
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1413 | (4) |
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[1914f] On cyclotomic quinquisection |
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1417 | (10) |
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[1915a] On periodic irrotational waves at the surface of deep water |
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1427 | (6) |
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[1915b] On the steady motion of fluid under gravity |
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1433 | (4) |
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[1916a] Determinants of cyclically repeated arrays |
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1437 | (4) |
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[1916b] On the efficiency of a surface of pressure discontinuity regarded as a propeller |
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1441 | (12) |
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[1917a] A rapidly convergent series for log N! |
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1453 | (4) |
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[1917b] An approximate expression for Σ∞n=0 1/(m+n)r |
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1457 | (4) |
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[1917c] An expression for the remainder in the expansion of a function in a series of positive integral powers of the variables |
|
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1461 | (4) |
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[1917d] On rational approximations to log x |
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1465 | (2) |
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[1918a] On a plane configuration of points and lines connected with the group of 168 plane collineations |
|
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1467 | (2) |
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[1918b] On the probable regularity of a random distribution of points |
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1469 | (2) |
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[1919a] On certain plane configurations of points and lines |
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1471 | (4) |
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[1919b] A property of groups of even order |
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1475 | (2) |
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[1919c] On a property of algebraic numbers |
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1477 | (2) |
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[1920a] On cyclical octosection |
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1479 | (8) |
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[1920b] On the representation of the simple group of order 660 as a group of linear substitutions on 5 symbols |
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1487 | (4) |
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[1921a] Convex solids in higher space |
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1491 | (6) |
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[1921b] On certain simply-transitive permutation-groups |
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1497 | (4) |
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[1923a] On errors of observation |
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1501 | (6) |
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[1923b] On rational approximations to cyclical cubic irrationalities |
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1507 | (4) |
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[1923c] The solution of a certain partial difference equation |
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1511 | (4) |
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[1923d] On a spherical configuration of eight points |
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1515 | (4) |
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[1923e] On the formulae of one-dimensional kinematics |
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1519 | (6) |
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[1923f] On errors of observation |
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1525 | (2) |
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[1924a] On an integral connected with the theory of probability |
|
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1527 | (4) |
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[1924b] On a partial linear difference equation |
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1531 | (6) |
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[1924c] On the polygons inscribed in one conic and circumscribed to another |
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1537 | (4) |
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[1924d] The problems of random flight and conduction of heat |
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1541 | (2) |
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[1925a] On the phrase ``equally probable'' |
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1543 | (4) |
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[1925b] On the relation connecting the 10 distances between 5 points in space |
|
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1547 | (2) |
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[1925c] On the approximate sum of selected terms from the multinomial expansion |
|
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1549 | (4) |
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[1925d] On the idea of frequency |
|
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1553 | (2) |
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[1925e] On the representation of the modular group of order 1/2p(p2 -- 1) as a group of linear substitutions on 1/2 (p -- 1) symbols, when p is a prime of the form 4n + 3 |
|
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1555 | (10) |
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[1925f] On groups of linear substitutions which contain irreducible metacyclical subgroups |
|
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1565 | (6) |
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[1926a] On a group of 1440 birational transformations of four variables that arises in considering the projective equivalence of double sixes |
|
|
1571 | (6) |
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[1926b] On the ``hypothetical infinite population'' of theoretical statistics |
|
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1577 | (6) |
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[1926c] On a group of order 25920 and the projective transformations of a cubic surface |
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1583 | |
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