© 2009

A Course on Finite Groups


Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-XII
  2. H. E. Rose
    Pages 1-10
  3. H. E. Rose
    Pages 11-40
  4. H. E. Rose
    Pages 41-65
  5. H. E. Rose
    Pages 67-90
  6. H. E. Rose
    Pages 113-137
  7. H. E. Rose
    Pages 139-163
  8. H. E. Rose
    Pages 165-185
  9. H. E. Rose
    Pages 209-227
  10. H. E. Rose
    Pages 229-247
  11. H. E. Rose
    Pages 249-275
  12. H. E. Rose
    Pages 277-295
  13. Back Matter
    Pages 297-311

About this book


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, 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.


Abelian group Group representation Group theory Representation theory algebra character table character theory

Authors and affiliations

  1. 1.School of MathematicsBristol UniversityBristolUnited Kingdom

Bibliographic information


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)