Grundlehren der mathematischen Wissenschaften

Cohomology of Finite Groups

Authors: Adem, Alejandro, Milgram, R. James

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About this book

The cohomology of groups has, since its beginnings in the 1920s and 1930s, been the stage for significant interaction between algebra and topology and has led to the creation of important new fields in mathematics, like homological algebra and algebraic K-theory.

This is the first book to deal comprehensively with the cohomology of finite groups: it introduces the most important and useful algebraic and topological techniques, describing the interplay of the subject with those of homotopy theory, representation theory and group actions. The combination of theory and examples, together with the techniques for  computing the cohomology of various important classes of groups, and several of the sporadic simple groups, enables readers to acquire an in-depth understanding of group cohomology and its extensive applications.

The 2nd edition contains many more mod 2 cohomology calculations for the sporadic simple groups, obtained by the authors and with their collaborators over the past decade. -Chapter III on group cohomology and invariant theory has been revised and expanded. New references arising from recent developments in the field have been added, and the index substantially enlarged.

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)


Table of contents (11 chapters)

  • Introduction

    Adem, Alejandro (et al.)

    Pages 1-5

  • Group Extensions, Simple Algebras and Cohomology

    Adem, Alejandro (et al.)

    Pages 7-42

  • Classifying Spaces and Group Cohomology

    Adem, Alejandro (et al.)

    Pages 43-88

  • Invariants and Cohomology of Groups

    Adem, Alejandro (et al.)

    Pages 89-113

  • Spectral Sequences and Detection Theorems

    Adem, Alejandro (et al.)

    Pages 115-155

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-662-06280-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-540-20283-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-3-642-05785-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Cohomology of Finite Groups
Authors
Series Title
Grundlehren der mathematischen Wissenschaften
Series Volume
309
Copyright
2004
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-06280-7
DOI
10.1007/978-3-662-06280-7
Hardcover ISBN
978-3-540-20283-7
Softcover ISBN
978-3-642-05785-4
Series ISSN
0072-7830
Edition Number
2
Number of Pages
VIII, 324
Topics