Synopses & Reviews
This expertly written volume presents a useful, coherent account of the theory of the cohomology ring of a finite group. The book employs a modern approach from the point of view of homological algebra, and covers themes such as finite generation theorems, the cohomology of wreath products, the norm map, and variety theory. Prerequisites comprise a familiarity with modern algebra comparable to that offered in introductory graduate courses, although otherwise the book is self-contained. As a result, it will be useful for those already engaged or commencing research in this area of mathematics by providing an up-to-date survey of important techniques and their applications to finite group theory.
Review
"Covers a wide range of topics. The style is clear and concise. . . . it is definitely a most welcome and very valuable book to all those who already know some aspects of the cohomology theory of groups and who want to know more about it." --Mathematical Reviews
Synopsis
Cohomology of groups is a specialized topic, but it has figured prominently in major developments in important areas of mathematics. Its roots lie in both algebra and geometry.
Description
Includes bibliographical references (p. 147-152) and index.
Table of Contents
1. Preliminaries
2. Explicit Resolutions
3. Products in Cohomology
4. Relations to Cohomology of Subgroups
5. Cohomology of Wreath Products
6. The Norm Map
7. Spectral Sequences
8. Varieties and Complexity
9. Stratification
10. Some Related Theorems