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