Group theory is an important subject that has come a long way in recent years. Introduction to Group Theory presents the fundamentals of both finite and infinite group theory, with a focus on finite groups. It provides students with the ability to prove the Thomas normal p-complement theorem and to classify simple finite groups. A large portion of the text is devoted to general linear groups. Additional topics covered include the construction of BN pairs, Coexeter groups, Hall-Higham theory, and Bender results. The text also offers an in-depth exploration of the complex relationship between groups, coding, and cryptography.
University College, Oxford, England
Basic Concepts. Permutations and Group Actions. Sylow's Theorems. Direct and Semidirect Products. Groups with Operators. Soluble Groups. Nilpotent Groups. Transfer and Fusion. Free Groups and Presentations. Coxeter Groups. The General Linear Group. Representation Theory. p-Length Theorems. p-Local Subgroups and Control. The Generalized Fitting and Bender Subgroups.
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- ID: 9781584886211
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