Theory of Groups of Finite Order

William Burnside

doi:10.1017/CBO9781139237253

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William Burnside

Publisher:: Cambridge University Press
Online publication date:: May 2013
Print publication year:: 2012
First published in:: 1897
Online ISBN:: 9781139237253
DOI:: https://doi.org/10.1017/CBO9781139237253

Subjects:: Mathematics (general), Mathematics, History of Mathematical Texts, Number Theory
Series:: Cambridge Library Collection - Mathematics

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The British mathematician William Burnside (1852–1927) and Ferdinand Georg Frobenius (1849–1917), Professor at Zurich and Berlin universities, are considered to be the founders of the modern theory of finite groups. Not only did Burnside prove many important theorems, but he also laid down lines of research for the next hundred years: two Fields Medals have been awarded for work on problems suggested by him. The Theory of Groups of Finite Order, originally published in 1897, was the first major textbook on the subject. The 1911 second edition (reissued here) contains an account of Frobenius's character theory, and remained the standard reference for many years.

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Theory of Groups of Finite Order

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Frontmatter
pp i-iv

PREFACE TO THE SECOND EDITION
pp v-vi

PREFACE TO THE FIRST EDITION
pp vii-x

Contents
pp xi-xxiv

CHAPTER I - ON PERMUTATIONS
pp 1-10

CHAPTER II - THE DEFINITION OF A GROUP
pp 11-24

CHAPTER III - ON THE SIMPLER PROPERTIES OF A GROUP WHICH ARE INDEPENDENT OF ITS MODE OF REPRESENTATION
pp 25-45

CHAPTER IV - FURTHER PROPERTIES OF A GROUP WHICH ARE INDEPENDENT OF ITS MODE OF REPRESENTATION
pp 46-63

CHAPTER V - ON THE COMPOSITION-SERIES OF A GROUP
pp 64-80

CHAPTER VI - ON THE ISOMORPHISM OF A GROUP WITH ITSELF
pp 81-98

CHAPTER VII - ON ABELIAN GROUPS
pp 99-118

CHAPTER VIII - ON GROUPS WHOSE ORDERS ARE THE POWERS OF PRIMES
pp 119-148

CHAPTER IX - ON SYLOW'S THEOREM
pp 149-167

CHAPTER X - ON PERMUTATION-GROUPS: TRANSITIVE AND INTRANSITIVE GROUPS: PRIMITIVE AND IMPRIMITIVE GROUPS
pp 168-204

CHAPTER XI - ON PERMUTATION-GROUPS: TRANSITIVITY AND PRIMITIVITY: (CONCLUDING PROPERTIES)
pp 205-230

CHAPTER XII - ON THE REPRESENTATION OF A GROUP OF FINITE ORDER AS A PERMUTATION-GROUP
pp 231-242

CHAPTER XIII - ON GROUPS OF LINEAR SUBSTITUTIONS; REDUCIBLE AND IRREDUCIBLE GROUPS
pp 243-268

CHAPTER XIV - ON THE REPRESENTATION OF A GROUP OF FINITE ORDER AS A GROUP OF LINEAR SUBSTITUTIONS
pp 269-279

CHAPTER XV - ON GROUP-CHARACTERISTICS
pp 280-320

CHAPTER XVI - SOME APPLICATIONS OF THE THEORY OF GROUPS OF LINEAR SUBSTITUTIONS AND OF GROUP-CHARACTERISTICS
pp 321-354

CHAPTER XVII - ON THE INVARIANTS OF GROUPS OF LINEAR SUBSTITUTIONS
pp 355-371

CHAPTER XVIII - ON THE GRAPHICAL REPRESENTATION OF A GROUP
pp 372-401

CHAPTER XIX - ON THE GRAPHICAL REPRESENTATION OF GROUPS: GROUPS OF GENUS ZERO AND UNITY; CAYLEY'S COLOUR GROUPS
pp 402-427

CHAPTER XX - ON CONGRUENCE GROUPS
pp 428-460

NOTES
pp 461-506

INDEX OF TECHNICAL TERMS
pp 507-508

INDEX OF AUTHORS QUOTED
pp 508-508

GENERAL INDEX
pp 509-512

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