Theory of Groups of Finite Order

William Burnside

doi:10.1017/CBO9781139237253

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.

- Aa Reduce text
- Aa Enlarge text

View selected items
Save to my bookmarks
Export citations
Download PDF (zip)
Save to Kindle
Save to Dropbox
Save to Google Drive
Save content to
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to .

To save content items to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Please be advised that item(s) you selected are not available.
You are about to save
Your Kindle email address

Please provide your Kindle email.

@free.kindle.com @kindle.com (service fees apply)

By using this service, you agree that you will only keep content for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services

Contents

Frontmatter
pp i-iv
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

PREFACE TO THE SECOND EDITION
pp v-vi
- By W. Burnside
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

PREFACE TO THE FIRST EDITION
pp vii-x
- By W. Burnside
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Contents
pp xi-xxiv
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

CHAPTER I - ON PERMUTATIONS
pp 1-10
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

CHAPTER II - THE DEFINITION OF A GROUP
pp 11-24
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

CHAPTER III - ON THE SIMPLER PROPERTIES OF A GROUP WHICH ARE INDEPENDENT OF ITS MODE OF REPRESENTATION
pp 25-45
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

CHAPTER IV - FURTHER PROPERTIES OF A GROUP WHICH ARE INDEPENDENT OF ITS MODE OF REPRESENTATION
pp 46-63
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

CHAPTER V - ON THE COMPOSITION-SERIES OF A GROUP
pp 64-80
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

CHAPTER VI - ON THE ISOMORPHISM OF A GROUP WITH ITSELF
pp 81-98
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

CHAPTER VII - ON ABELIAN GROUPS
pp 99-118
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

CHAPTER VIII - ON GROUPS WHOSE ORDERS ARE THE POWERS OF PRIMES
pp 119-148
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

CHAPTER IX - ON SYLOW'S THEOREM
pp 149-167
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

CHAPTER X - ON PERMUTATION-GROUPS: TRANSITIVE AND INTRANSITIVE GROUPS: PRIMITIVE AND IMPRIMITIVE GROUPS
pp 168-204
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

CHAPTER XI - ON PERMUTATION-GROUPS: TRANSITIVITY AND PRIMITIVITY: (CONCLUDING PROPERTIES)
pp 205-230
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

CHAPTER XII - ON THE REPRESENTATION OF A GROUP OF FINITE ORDER AS A PERMUTATION-GROUP
pp 231-242
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

CHAPTER XIII - ON GROUPS OF LINEAR SUBSTITUTIONS; REDUCIBLE AND IRREDUCIBLE GROUPS
pp 243-268
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

CHAPTER XIV - ON THE REPRESENTATION OF A GROUP OF FINITE ORDER AS A GROUP OF LINEAR SUBSTITUTIONS
pp 269-279
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

CHAPTER XV - ON GROUP-CHARACTERISTICS
pp 280-320
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

CHAPTER XVI - SOME APPLICATIONS OF THE THEORY OF GROUPS OF LINEAR SUBSTITUTIONS AND OF GROUP-CHARACTERISTICS
pp 321-354
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

CHAPTER XVII - ON THE INVARIANTS OF GROUPS OF LINEAR SUBSTITUTIONS
pp 355-371
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

CHAPTER XVIII - ON THE GRAPHICAL REPRESENTATION OF A GROUP
pp 372-401
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

CHAPTER XIX - ON THE GRAPHICAL REPRESENTATION OF GROUPS: GROUPS OF GENUS ZERO AND UNITY; CAYLEY'S COLOUR GROUPS
pp 402-427
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

CHAPTER XX - ON CONGRUENCE GROUPS
pp 428-460
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

NOTES
pp 461-506
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

INDEX OF TECHNICAL TERMS
pp 507-508
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

INDEX OF AUTHORS QUOTED
pp 508-508
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

GENERAL INDEX
pp 509-512
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Metrics

Total number of HTML views: 0

Total number of PDF views: 0 *

Loading metrics...

Total views: 0 *

Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.

Why this information is here

This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.

Accessibility Information

Accessibility compliance for the PDF of this book is currently unknown and may be updated in the future.

Theory of Groups of Finite Order

This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

Book description

Refine List

Actions for selected content:

Contents

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

Metrics

Full text views

Book summary page views

Accessibility standard: Unknown

Why this information is here

Accessibility Information

Theory of Groups of Finite Order

Book description

Refine List

Actions for selected content:

Save Search

Contents

Metrics

Full text views

Book summary page views

Accessibility standard: Unknown

Why this information is here

Accessibility Information