Cohomology Rings of Finite Groups: with an Appendix: Calculations of Cohomology Rings of Groups of Order Dividing 64 [Hardcover]

Jon F. Carlson (Author), L. Townsley (Author), Lu�s Valero-Elizondo (Author), Mucheng Zhang (Author)

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Product Details

Hardcover: 776 pages
Publisher: Springer; 1 edition (Oct 31 2003)
Language: English
ISBN-10: 1402015259
ISBN-13: 978-1402015250
Product Dimensions: 24.4 x 16.3 x 5.1 cm
Shipping Weight: 1.5 Kg
Amazon Bestsellers Rank: #2,049,883 in Books (See Top 100 in Books)

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Review

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)

Product Description

This text offers comprehensive coverage of group cohomology, from introductory material through the most recent developments in the field. The primary motivation for this book is the interaction of group cohomology with representation theory, especially the geometry of support varieties over cohomology rings. The appendices, comprising computer calculations of the mod-2 cohomology rings of the groups whose orders divide 64, provide information useful for further developments in the field. A unique feature of this text is that it includes the concepts that are the subject of the calculations and are the source of some of the motivating conjectures for the computations. The programs for computing the cohomology rings were executed in the MAGMA computer algebra language. The text is a valuable resource for researchers in group cohomology and related disciplines. In addition, the book could be used as the text for an advanced graduate class or a graduate seminar.

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First Sentence
Proof. To show the existence of a pushout in the module category for a diagram as above, we define the module X = (M N)/I where I = { }. Read the first page

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