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Cohomology of Finite Groups

  • Book
  • © 2004

Overview

Authors:
  1. Alejandro Adem

    1. Department of Mathematics, Van Vleck Hall, University of Wisconsin, Madison, USA

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  2. R. James Milgram

    1. Department of Mathematics, Stanford University, Stanford, USA

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 309)

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Table of contents (11 chapters)

  1. Front Matter

    Pages I-VIII
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  2. Introduction

    • Alejandro Adem, R. James Milgram
    Pages 1-5

  3. Group Extensions, Simple Algebras and Cohomology

    • Alejandro Adem, R. James Milgram
    Pages 7-42

  4. Classifying Spaces and Group Cohomology

    • Alejandro Adem, R. James Milgram
    Pages 43-88

  5. Invariants and Cohomology of Groups

    • Alejandro Adem, R. James Milgram
    Pages 89-113

  6. Spectral Sequences and Detection Theorems

    • Alejandro Adem, R. James Milgram
    Pages 115-155

  7. G-Complexes and Equivariant Cohomology

    • Alejandro Adem, R. James Milgram
    Pages 157-174

  8. The Cohomology of the Symmetric Groups

    • Alejandro Adem, R. James Milgram
    Pages 175-212

  9. Finite Groups of Lie Type

    • Alejandro Adem, R. James Milgram
    Pages 213-243

  10. Cohomology of Sporadic Simple Groups

    • Alejandro Adem, R. James Milgram
    Pages 245-271

  11. The Plus Construction and Applications

    • Alejandro Adem, R. James Milgram
    Pages 273-286

  12. The Schur Subgroup of the Brauer Group

    • Alejandro Adem, R. James Milgram
    Pages 287-313

  13. Back Matter

    Pages 315-326
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Keywords

About this book

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

Reviews

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)

Authors and Affiliations

  • Department of Mathematics, Van Vleck Hall, University of Wisconsin, Madison, USA

    Alejandro Adem

  • Department of Mathematics, Stanford University, Stanford, USA

    R. James Milgram

Bibliographic Information

  • Book Title: Cohomology of Finite Groups

  • Authors: Alejandro Adem, R. James Milgram

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-3-662-06280-7

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2004

  • Hardcover ISBN: 978-3-540-20283-7Published: 02 December 2003

  • Softcover ISBN: 978-3-642-05785-4Published: 01 December 2010

  • eBook ISBN: 978-3-662-06280-7Published: 14 March 2013

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 2

  • Number of Pages: VIII, 324

  • Topics: Algebra, Group Theory and Generalizations, Algebraic Topology, K-Theory

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