Pub. Date:
Springer Berlin Heidelberg
Cohomology of Finite Groups / Edition 2

Cohomology of Finite Groups / Edition 2

by Alejandro Adem, R. James Milgram


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Cohomology of Finite Groups / Edition 2

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

Product Details

ISBN-13: 9783642057854
Publisher: Springer Berlin Heidelberg
Publication date: 12/08/2010
Series: Grundlehren der mathematischen Wissenschaften , #309
Edition description: Softcover reprint of hardcover 2nd ed. 2004
Pages: 324
Product dimensions: 6.10(w) x 9.25(h) x 0.24(d)

Table of Contents

I. Group Extensions, Simple Algebras and Cohomology.- II. Classifying Spaces and Group Cohomology.- III. Invariants and Cohomology of Groups.- IV. Spectral Sequences and Detection Theorems.- V. G-Complexes and Equivariant Cohomology.- VI. The Cohomology of the Symmetric Groups.- VII. Finite Groups of Lie Type.- VIII. Cohomology of Sporadic Simple Groups.- IX. The Plus Construction and Applications.- X. The Schur Subgroup of the Brauer Group.- References.

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