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Cohomology of Finite Groups : Grundlehren der mathematischen Wissenschaften - Alejandro Adem

Cohomology of Finite Groups

Grundlehren der mathematischen Wissenschaften

Hardcover Published: 2nd December 2003
ISBN: 9783540202837
Number Of Pages: 324

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Some Historical Background This book deals with the cohomology of groups, particularly finite ones. Historically, the subject has been one of significant interaction between algebra and topology and has directly led to the creation of such important areas of mathematics as homo­ logical algebra and algebraic K-theory. It arose primarily in the 1920's and 1930's independently in number theory and topology. In topology the main focus was on the work ofH. Hopf, but B. Eckmann, S. Eilenberg, and S. MacLane (among others) made significant contributions. The main thrust of the early work here was to try to understand the meanings of the low dimensional homology groups of a space X. For example, if the universal cover of X was three connected, it was known that H2(X; A. ) depends only on the fundamental group of X. Group cohomology initially appeared to explain this dependence. In number theory, group cohomology arose as a natural device for describing the main theorems of class field theory and, in particular, for describing and analyzing the Brauer group of a field. It also arose naturally in the study of group extensions, N

From the reviews of the second edition:

"This book is very different from other treatments since it emphasizes the computational aspects of the cohomology of finite groups with coefficients in a field. ... I say merely that each mathematician interested in algebra and topology should have a copy of this book on their shelf and make sure that their librarian gets one as well. Overall I thoroughly recommend this book and believe that it will be a useful book for introducing students to cohomological methods for groups." (Manuel Ladra Gonzalez, Zentralblatt MATH, Vol. 1061 (12), 2005)

Introductionp. 1
Group Extensions, Simple Algebras and Cohomologyp. 7
Classifying Spaces and Group Cohomologyp. 43
Invariants and Cohomology of Groupsp. 89
Spectral Sequences and Detection Theoremsp. 115
G-Complexes and Equivariant Cohomologyp. 157
The Cohomology of the Symmetric Groupsp. 175
Finite Groups of Lie Typep. 213
Cohomology of Sporadic Simple Groupsp. 245
The Plus Construction and Applicationsp. 273
The Schur Subgroup of the Brauer Groupp. 287
Referencesp. 315
Indexp. 321
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540202837
ISBN-10: 3540202838
Series: Grundlehren der mathematischen Wissenschaften
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 324
Published: 2nd December 2003
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.9 x 16.0  x 2.3
Weight (kg): 0.65
Edition Number: 2
Edition Type: Revised

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