Profinite Groups / Edition 1

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Overview

Profinite groups are of interest to mathematicians working in a variety of areas, including number theory, abstract groups, and analysis. The underlying theory reflects these diverse influences, with methods drawn from both algebra and topology and with fascinating connections to field theory. This is the first book to be dedicated solely to the study of general profinite groups. It provides a thorough introduction to the subject, designed not only to convey the basic facts but also to enable readers to enhance their skills in manipulating profinite groups. The first few chapters lay the foundations and explain the role of profinite groups in number theory. Later chapters explore various aspects 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.

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Product Details

  • ISBN-13: 9780198500827
  • Publisher: Oxford University Press, USA
  • Publication date: 1/28/1999
  • Series: London Mathematical Society Monographs Series , #19
  • Edition number: 1
  • Pages: 296
  • Product dimensions: 6.10 (w) x 9.30 (h) x 0.90 (d)

Table of Contents

Leitfaden
Notational and terminological conventions
0 Topological preliminaries 1
1 Profinite groups and completions 11
2 Sylow theory 34
3 Galois theory 47
4 Finitely generated groups and countably based groups 53
5 Free groups and projective groups 68
6 Modules, extensions and duality 94
7 Modules for completed group algebras 114
8 Profinite groups of finite rank 138
9 Cohomology of profinite groups 164
10 Further cohomological methods 191
11 Groups of finite cohomological dimension 210
12 Finitely presented pro-p groups 238
Bibliography 274
Index 281
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