Course on Finite Groups (eBook)

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 on more challenging and more specialised topics can be used as extension material for courses, or for further independent study.

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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 "e;actual"e; 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.