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.

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. Includes supplementary material: sn.pub/extras

Inhalt
IntroductionThe Group Concept.- Elementary Group Properties.- Group Construction and Representation.- Homomorphisms.- Action and the OrbitStabiliser Theorem.- -Groups and Sylow Theory.- Products and Abelian Groups.- Groups of Order 24 Three Examples.- Series, JordanHölder Theorem and the Extension Problem.- Nilpotency.- Solubility.- Simple Groups of Order Less than 10000.- Appendices A to E.