A Course on Finite Groups (Universitext) - Softcover

Rose, H.E.

Softcover

ISBN 10: 1848828888 ISBN 13: 9781848828889

Publisher: Springer, 2010

Synopsis

Group Theory has wide-ranging uses in the field of mathematics. This book offers a comprehensive account of the finite groups. It begins with the basic definitions and moves on to develop the theory, using examples to help students with their understanding.

About this title

From the Back Cover

A Course on Finite Groups introduces the fundamentals of group theory to advanced undergraduate and beginning graduate students. Based on a series of lecture courses developed by the author over many years, the book starts with the basic definitions and examples and develops the theory to the point where a number of classic theorems can be proved. The topics covered include: group constructions; homomorphisms and isomorphisms; actions; Sylow theory; products and Abelian groups; series; nilpotent and soluble groups; and an introduction to the classification of the finite simple groups.

A number of groups are described in detail and the reader is encouraged to work with one of the many computer algebra packages available to construct and experience "actual" groups for themselves in order to develop a deeper understanding of the theory and the significance of the theorems. Numerous problems, of varying levels of difficulty, help to test understanding.

A brief resumé of the basic set theory and number theory required for the text is provided in an appendix, and a wealth of extra resources is available online at www.springer.com, including: hints and/or full solutions to all of the exercises; extension material for many of the chapters, covering more challenging topics and results for further study; and two additional chapters providing an introduction to group representation theory.

Edition details

• Publisher: Springer
• Publication date: 2010
• Language: English
• ISBN 10: 1848828888
• ISBN 13: 9781848828889
• Binding: Paperback
• Number of pages: 323