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  • © 2003

Cohomology Rings of Finite Groups

With an Appendix: Calculations of Cohomology Rings of Groups of Order Dividing 64

Part of the book series: Algebra and Applications (AA, volume 3)

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xv
  2. Homological Algebra

    • Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo, Mucheng Zhang
    Pages 1-22
  3. Group Algebras

    • Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo, Mucheng Zhang
    Pages 23-46
  4. Projective Resolutions

    • Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo, Mucheng Zhang
    Pages 47-59
  5. Cohomology Products

    • Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo, Mucheng Zhang
    Pages 61-85
  6. Spectral Sequences

    • Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo, Mucheng Zhang
    Pages 87-110
  7. Norms and the Cohomology of Wreath Products

    • Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo, Mucheng Zhang
    Pages 111-128
  8. Steenrod Operations

    • Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo, Mucheng Zhang
    Pages 129-157
  9. Varieties and Elementary Abelian Subgroups

    • Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo, Mucheng Zhang
    Pages 159-177
  10. Cohomology Rings of Modules

    • Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo, Mucheng Zhang
    Pages 179-208
  11. Complexity and Multiple Complexes

    • Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo, Mucheng Zhang
    Pages 209-230
  12. Duality Complexes

    • Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo, Mucheng Zhang
    Pages 231-253
  13. Transfers, Depth and Detection

    • Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo, Mucheng Zhang
    Pages 255-282
  14. Subgroup Complexes

    • Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo, Mucheng Zhang
    Pages 283-312
  15. Computer Calculations and Completion Tests

    • Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo, Mucheng Zhang
    Pages 313-335
  16. Back Matter

    Pages 337-777

About this book

Group cohomology has a rich history that goes back a century or more. Its origins are rooted in investigations of group theory and num­ ber theory, and it grew into an integral component of algebraic topology. In the last thirty years, group cohomology has developed a powerful con­ nection with finite group representations. Unlike the early applications which were primarily concerned with cohomology in low degrees, the in­ teractions with representation theory involve cohomology rings and the geometry of spectra over these rings. It is this connection to represen­ tation theory that we take as our primary motivation for this book. The book consists of two separate pieces. Chronologically, the first part was the computer calculations of the mod-2 cohomology rings of the groups whose orders divide 64. The ideas and the programs for the calculations were developed over the last 10 years. Several new features were added over the course of that time. We had originally planned to include only a brief introduction to the calculations. However, we were persuaded to produce a more substantial text that would include in greater detail the concepts that are the subject of the calculations and are the source of some of the motivating conjectures for the com­ putations. We have gathered together many of the results and ideas that are the focus of the calculations from throughout the mathematical literature.

Reviews

From the reviews:

"The cohomology of groups was developed to be … a powerful tool in the study of group representations. … Some other books concerning the cohomology of finite groups have appeared, but they are at least ten years old, and the computational tools that have been developed since then, make this book to be really valuable for both professionals and students. … This book is almost self-contained and it is very useful … for all of those that are using the cohomology instruments in their work." (Viorel Mihai Gontineac, Zentralblatt MATH, Vol. 1056 (7), 2005)

Authors and Affiliations

  • University of Georgia, Athens, USA

    Jon F. Carlson, Mucheng Zhang

  • Benedictine University, Lisle, USA

    Lisa Townsley

  • Instituto de Matematicas, UNAM, Morelia, USA

    Luis Valeri-Elizondo

Bibliographic Information

  • Book Title: Cohomology Rings of Finite Groups

  • Book Subtitle: With an Appendix: Calculations of Cohomology Rings of Groups of Order Dividing 64

  • Authors: Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo, Mucheng Zhang

  • Series Title: Algebra and Applications

  • DOI: https://doi.org/10.1007/978-94-017-0215-7

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 2003

  • Hardcover ISBN: 978-1-4020-1525-0Published: 31 October 2003

  • Softcover ISBN: 978-90-481-6385-4Published: 09 December 2010

  • eBook ISBN: 978-94-017-0215-7Published: 17 April 2013

  • Series ISSN: 1572-5553

  • Series E-ISSN: 2192-2950

  • Edition Number: 1

  • Number of Pages: XVI, 776

  • Topics: Geometry, Category Theory, Homological Algebra, Algebra, Commutative Rings and Algebras, Numeric Computing, Algebraic Topology

Buy it now

Buying options

eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access