A Course on Finite Groups (Universitext) (Paperback)

A Course on Finite Groups (Universitext) By H. E. Rose Cover Image

A Course on Finite Groups (Universitext) (Paperback)


Not On Our Shelves—Ships in 1-5 Days
(This book cannot be returned.)

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: Lagrange's theorem; group constructions; homomorphisms and isomorphisms; actions; Sylow theory, products and Abelian groups; series, and 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 exercises, of varying levels of difficulty, help to test understanding.

A brief resum 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.

Product Details ISBN: 9781848828889
ISBN-10: 1848828888
Publisher: Springer
Publication Date: February 4th, 2010
Pages: 311
Language: English
Series: Universitext