A Course on Group Theory

John S. Rose

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English

Dover Publications Inc.
13 June 2012

Mathematics & Sciences; Groups & group theory

Series: Dover Books on Mathema 1.4tics

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.

By: John S. Rose
Imprint: Dover Publications Inc.
Country of Publication: United States
Edition: New edition
Dimensions: Height: 220mm, Width: 142mm, Spine: 15mm
Weight: 395g
ISBN: 9780486681948
ISBN 10: 0486681947
Series: Dover Books on Mathema 1.4tics
Pages: 320
Publication Date: 13 June 2012
Audience: General/trade , ELT Advanced
Format: Paperback
Publisher's Status: Unspecified

"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"

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