A Course on Group Theory

by John S. Rose

Overview

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.

Product Details

ISBN-13:	9780486681948
Publisher:	Dover Publications
Publication date:	06/13/2012
Series:	Dover Books on Mathematics
Edition description:	Revised ed.
Pages:	320
Product dimensions:	5.30(w) x 8.40(h) x 0.80(d)

About the Author

The late John S. Rose was Senior Lecturer in Pure Mathematics at England's University of Newcastle upon Tyne.

Table of Contents

Preface
0 Some conventions and some basic facts
1 Introduction to finite group theory
2 Examples of groups and homomorphisms
3 "Normal subgroups, homomorphisms and quotients"
4 Group actions on sets
5 Finite p-groups and Sylow's theorem
6 Groups of even orders
7 Series
8 Direct products and the structure of finitely generated abelian groups
9 Group actions on groups
10 Transfer and splitting theorems
11 Finite nilpotent and soluble groups
References
Index of notation
Index of subjects