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Cohomology Rings of Finite Groups

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

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

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

Table of contents

  1. Front Matter
    Pages i-xv
  2. Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo, Mucheng Zhang
    Pages 1-22
  3. Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo, Mucheng Zhang
    Pages 23-46
  4. Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo, Mucheng Zhang
    Pages 47-59
  5. Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo, Mucheng Zhang
    Pages 61-85
  6. Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo, Mucheng Zhang
    Pages 87-110
  7. Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo, Mucheng Zhang
    Pages 111-128
  8. Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo, Mucheng Zhang
    Pages 129-157
  9. Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo, Mucheng Zhang
    Pages 159-177
  10. Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo, Mucheng Zhang
    Pages 179-208
  11. Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo, Mucheng Zhang
    Pages 209-230
  12. Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo, Mucheng Zhang
    Pages 231-253
  13. Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo, Mucheng Zhang
    Pages 255-282
  14. Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo, Mucheng Zhang
    Pages 283-312
  15. Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo, Mucheng Zhang
    Pages 313-335
  16. Back Matter
    Pages 337-777

About this book

Introduction

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.

Keywords

Abelian group Algebra Cohomology Computer Homological algebra Representation theory complexity computer algebra homology

Authors and affiliations

  • Jon F. Carlson
    • 1
  • Lisa Townsley
    • 2
  • Luis Valeri-Elizondo
    • 3
  • Mucheng Zhang
    • 1
  1. 1.University of GeorgiaAthensUSA
  2. 2.Benedictine UniversityLisleUSA
  3. 3.Instituto de MatematicasUNAMMoreliaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-0215-7
  • Copyright Information Springer Science+Business Media B.V. 2003
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-6385-4
  • Online ISBN 978-94-017-0215-7
  • Series Print ISSN 1572-5553
  • Series Online ISSN 2192-2950
  • Buy this book on publisher's site
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