The Collected Papers of William Burnside 2-Volume Set

by Burnside, William; Neumann, Peter M.; Mann, A. J. S.; Tompson, Julia C.

• ISBN13: 9780198505853
• ISBN10: 019850585X
• Format: Hardcover
• Copyright: 2004-11-18
• Publisher: Clarendon Press

Summary

William 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.

Table of Contents

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