## The Collected Papers of William Burnside: Commentary on Burnside's life and work ; Papers 1883-1899William Burnside was one of the three most important algebraists who were involved in the transformation of group theory from its nineteenth-century origins to a deep twentieth-century subject. Building on work of earlier mathematicians, they were able to develop sophisticated tools for solving difficult problems. All of Burnside's papers are reproduced here, organized chronologically and with a detailed bibliography. Walter Feit has contributed a foreword, and a collection of introductory essays are included to provide a commentary on Burnside's work and set it in perspective along with a modern biography that draws on archive material. |

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### Contents

Bibliography of William Burnside | 7 |

1902g Theory of groups Encyclopaedia article 959 | 10 |

1914a On the rational solutions of the equation X3 + y3 + Z3 0 in quadratic fields 1393 | 12 |

The context of Burnsides contributions to group theory | 17 |

A still unsettled question | 39 |

Burnside and finite simple groups | 45 |

Burnsides research on representation theory | 55 |

Burnsides applied mathematics | 63 |

1892f Note on pseudoelliptic integrals | 337 |

1892g On the division of the periods of elliptic functions by 9 | 345 |

1892h Note on the equation v2 x x4 | 353 |

1893b Note on linear substitutions | 377 |

1893d Note on functions of a real variable | 385 |

1893f On the curve of intersection of two quadrics | 397 |

1893h On a property of certain determinants | 411 |

1894b On an application of the theory of groups to Kirkmans problem | 423 |

William Burnside reprinted from the Journal of the London Mathematical Society Vol 3 1928 | 71 |

Notes on Burnsides life | 89 |

The Papers 18831899 | 111 |

1883b Note on centre of pressure of a plane polygon | 117 |

1887a On the trisection of the periods for Weierstrasss elliptic functions | 125 |

1888b Note on the potential of an elliptic cylinder | 141 |

1888c On deepwater waves resulting from a limited original disturbance | 147 |

1889a On the small wavemotions of a heterogeneous fluid under gravity | 163 |

Geometrical interpretation of a condition of integrability | 169 |

1889e On the resultant of two finite displacements of a rigid body | 179 |

1890a On the differential equation of confocal spheroconics | 185 |

1890c On a property of plane isothermal curves | 197 |

11890d Note on a paper relating to the theory of functions | 203 |

b Note on the addition theorem for hyperbolic functions | 209 |

1891d On functions determined from their discontinuities and a certain form of boundary condition | 217 |

1891e On a certain Riemanns surface | 231 |

f On the form of closed curves of the third class | 239 |

Forms of the addition equation 2 On Pu considered | 245 |

1892a On the form of hyperelliptic integrals of the first order which are expressible as the | 289 |

1892b On the application of Abels theorem to elliptic integrals of the first kind | 303 |

1892c On the linear transformation of the elliptic differential | 311 |

1892d Prof Burnsides paper on the partition of energy R S E July 1887 | 319 |

1894c On a class of groups defined by congruences | 431 |

11894d On a system of linear congruences | 459 |

1894e On certain composite groups | 467 |

1894f On the kinematics of nonEuclidean space | 483 |

1894g Note on ternary substitutions of determinant unity with integral coefficients | 507 |

1895a Notes on the theory of groups of finite order Notes IIIVII | 561 |

1895b Correction to a former paper 1893e | 587 |

1895d On two theorems in elementary kinematics | 603 |

1896b On the isomorphism of a group with itself | 615 |

1896c On doublytransitive groups of degree 2m and order 2m 2m 1 | 629 |

1897b The construction of the straight line joining two given points | 645 |

1898al On the continuous group that is defined by any given group of finite order | 653 |

1898a2J On the continuous group that is defined by any given group of finite order second paper | 671 |

1898b On plane equipotential surfaces | 693 |

1898c On linear homogeneous continuous groups whose operations are permutable | 703 |

1898d Note on the simple group of order 504 | 731 |

1898f On the representation of a group of finite order as a substitution group | 741 |

1898h Correction to the paper on the representation of a group of finite order as a substitution | 747 |

1899a On the reduction of a linear substitution to its canonical form | 753 |

11899b Sketch of the late Prof Sophus Lies mathematical work | 769 |

1899c2 Discussion on Theory of Functions untitled letter | 779 |

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### Common terms and phrases

Abelian group algebraical axes axis Burnside problem Burnside's Burnside's theorem Cambridge character theory circles coefficients College congruence conjugate set conjugate sub-groups corresponding cosh curves cyclical sub-group determinant displacement equivalent expressed factor finite group finite order follows Frobenius given group G group of finite group of linear group of order group theory groups of odd groups whose orders Hence identical infinite number infinitesimal operations infinity integral inverse irreducible isomorphism linear substitutions lines lines of curvature London Math Messenger Math multiple normal subgroup odd order operation of G operations of order paper parameters Pembroke permutation groups plane polygon prime Proc proof quantities representation result Riemann's surface right angles roots rotation self-conjugate sub-group solution spheres sub-group of order surface Sylow Sylow subgroups symmetric group theorem theory of groups transformed translation triangle unchanged unity values variables William Burnside zero