Profinite Groups

by Wilson, John S.

• ISBN13: 9780198500827
• ISBN10: 0198500823
• Format: Hardcover
• Copyright: 1999-01-14
• Publisher: Clarendon Press

Summary

This is the first book to be dedicated entirely to profinite groups, an area of algebra with important links to number theory and other areas of mathematics. It provides a comprehensive overview of the subject; prerequisite knowledge is kept to a minimum, and several major theorems arepresented in an accessible form. The book would provide a valuable introduction for postgraduate students, or form a useful reference for researchers in other areas. The first few chapters lay the foundations and explain the role of profinite groups in number theory. Later chapters explore variousaspects of profinite groups in more detail; these contain accessible and lucid accounts of many major theorems. Prerequisites are kept to a minimum with the basic topological theory summarized in an introductory chapter.

Table of Contents

Topological preliminaries

Profinite groups and completions

Sylow theory

Galois theory

Finitely generated groups and countably based groups

Free groups and projective groups

Modules, extensions, and duality

Modules for completed group algebras

Profinite groups of finite rank

Cohomology of profinite groups

Further cohomological methods

Groups of finite cohomological dimension

Finitely present pro-p groups

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