Universitext

A Course on Finite Groups

Authors: Rose, H.E.

  • Introduces the richness of group theory to advanced undergraduate and graduate students, concentrating on the finite aspects.
  • Provides a wealth of exercises and problems to support self-study.
  • Additional online resources offer more challenging and more specialised topics which can be used as extension material for courses, or for further independent study.
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eBook $44.99
price for USA (gross)
  • ISBN 978-1-84882-889-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.95
price for USA
  • ISBN 978-1-84882-888-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

Reviews

From the reviews:

 “This is a self-contained introduction to the theory of finite groups. The treatment is exhaustive, from the elementary basic results up to characters and representations of finite groups … . main results are accompanied by several well-chosen examples, and there are many computations with groups of small order, giving the reader a sense of concreteness. … well-written book, not too wordy nor too terse. Concepts and results are illustrated with examples, and the problem sets at the end of every chapter nicely complement the theory.” (Felipe Zaldivar, The Mathematical Association of America, March, 2010)

“This book is an introduction to the finite group theory for undergraduate and beginning graduate mathematicians.” (Anatoli Kondrat’ev, Zentralblatt MATH, Vol. 1200, 2011)


Table of contents (13 chapters)

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-1-84882-889-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.95
price for USA
  • ISBN 978-1-84882-888-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
A Course on Finite Groups
Authors
Series Title
Universitext
Copyright
2009
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London
eBook ISBN
978-1-84882-889-6
DOI
10.1007/978-1-84882-889-6
Softcover ISBN
978-1-84882-888-9
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XII, 311
Topics