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A Course on Group Theory

Dover Books on Advanced Mathematics

Paperback

Published: 13th June 2012
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This textbook for advanced courses in group theory focuses on finite groups, with emphasis on the idea of group actions. Early chapters summarize presupposed facts, identify important themes, and establish the notation used throughout the book. Subsequent chapters explore the normal and arithmetical structures of groups as well as applications. Topics include the normal structure of groups: subgroups; homomorphisms and quotients; series; direct products and the structure of finitely generated Abelian groups; and group action on groups. Additional subjects range from the arithmetical structure of groups to classical notions of transfer and splitting by means of group action arguments. More than 675 exercises, many accompanied by hints, illustrate and extend the material. Dover 2012 reissue of the Dover 2007 reprint of the Cambridge University Press, Cambridge, England, 1978 edition

Preface
Some conventions and some basic facts
Introduction to finite group theory
Examples of groups and homomorphisms
"Normal subgroups, homomorphisms and quotients"
Group actions on sets
Finite p-groups and Sylow's theorem
Groups of even orders
Series
Direct products and the structure of finitely generated abelian groups
Group actions on groups
Transfer and splitting theorems
Finite nilpotent and soluble groups
References
Index of notation
Index of subjects
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780486681948
ISBN-10: 0486681947
Series: Dover Books on Advanced Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 320
Published: 13th June 2012
Dimensions (cm): 21.6 x 13.7  x 1.6
Weight (kg): 0.34