Profinite Groups / Edition 1

by John S. Wilson

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.

Product Details

ISBN-13:	9780198500827
Publisher:	Oxford University Press
Publication date:	01/14/1999
Series:	London Mathematical Society Monographs , #19
Pages:	296
Product dimensions:	6.40(w) x 9.40(h) x 1.00(d)

About the Author

School of Mathematics and Statistics, University of Birmingham

Table of Contents

0. Topological preliminaries1. Profinite groups and completions2. Sylow theory3. Galois theory4. Finitely generated groups and countably based groups5. Free groups and projective groups6. Modules, extensions, and duality7. Modules for completed group algebras8. Profinite groups of finite rank9. Cohomology of profinite groups10. Further cohomological methods11. Groups of finite cohomological dimension12. Finitely present pro-p groups