© 2004

Cohomology of Finite Groups


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

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Alejandro Adem, R. James Milgram
    Pages 1-5
  3. Alejandro Adem, R. James Milgram
    Pages 7-42
  4. Alejandro Adem, R. James Milgram
    Pages 43-88
  5. Alejandro Adem, R. James Milgram
    Pages 89-113
  6. Alejandro Adem, R. James Milgram
    Pages 115-155
  7. Alejandro Adem, R. James Milgram
    Pages 157-174
  8. Alejandro Adem, R. James Milgram
    Pages 175-212
  9. Alejandro Adem, R. James Milgram
    Pages 213-243
  10. Alejandro Adem, R. James Milgram
    Pages 245-271
  11. Alejandro Adem, R. James Milgram
    Pages 273-286
  12. Alejandro Adem, R. James Milgram
    Pages 287-313
  13. Back Matter
    Pages 315-326

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.


Algebraic K-theory Algebraic topology Cohomology K-theory algebra classifying spaces cohomology of groups group actions homological algebra homology homotopy theory

Authors and affiliations

  1. 1.Department of Mathematics, Van Vleck HallUniversity of WisconsinMadisonUSA
  2. 2.Department of MathematicsStanford UniversityStanfordUSA

Bibliographic information

  • Book Title Cohomology of Finite Groups
  • Authors Alejandro Adem
    R. James Milgram
  • Series Title Grundlehren der mathematischen Wissenschaften
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-20283-7
  • Softcover ISBN 978-3-642-05785-4
  • eBook ISBN 978-3-662-06280-7
  • Series ISSN 0072-7830
  • Edition Number 2
  • Number of Pages VIII, 324
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Algebra
    Group Theory and Generalizations
    Algebraic Topology
  • Buy this book on publisher's site


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)