The Collected Papers of William Burnside 2-Volume Set

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

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ISBN: 9780198505853 | 019850585X
Cover: Hardcover
Copyright: 11/18/2004

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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.

Preface

Acknowledgements

vii

List of contributors

Commentary on Burnside's Life and Work

(2)

Foreword

(4)

Water Feit

Bibliography of William Burnside

(8)

The context of Burnside's contributions to group theory

(24)

Peter M. Neumann

A still unsettled question

(6)

M. F. Newman

Burnside and finite simple groups

(10)

Ronald M. Solomon

Burnside's research on representation theory

(8)

Charles W. Curtis

Burnside's applied mathematics

(8)

June Barrow-Green

`William Burnside', reprinted from the Journal of the London Mathematical Society, Vol. 3 (1928)

(18)

A. R. Forsyth

Notes on Burnside's life

(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

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The Collected Papers of William Burnside 2-Volume Set

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