Description 
1 online resource (xii, 311 pages) : illustrations 
Series 
Universitext 

Universitext.

Contents 
The Group Concept  Elementary Group Properties  Group Construction and Representation  Homomorphisms  Action and the OrbitStabiliser Theorem  pGroups and Sylow Theory  Products and Abelian Groups  Groups of Order 24, Three Examples  Series, Jordan Hölder Theorem and the Extension Problem  Nilpotency  Solubility  Simple Groups of Order Less Than 10000  Representation and Character Theory  Character Tables and Theorems of Burnside and Frobenius  Appendices 
Summary 
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; Sylowtheory; 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 
Bibliography 
Includes bibliographical references (pages 297300) and index 
Notes 
English 

Print version record 
Subject 
Finite groups.

Form 
Electronic book

LC no. 
2009942898 
ISBN 
1848828896 (eisbn) 

9781848828896 (eisbn) 
