A Course on Finite Groups

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.

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

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)

• School of Mathematics, Bristol University, Bristol, United Kingdom

  H.E. Rose

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