| Cohomology of Finite Groups 2004 Edition Contributor(s): Adem, Alejandro (Author), Milgram, R. James (Author) |
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ISBN: 3540202838 ISBN-13: 9783540202837 Publisher: Springer OUR PRICE: $104.49 Product Type: Hardcover - Other Formats Published: December 2003 Annotation: The cohomology of groups has been the stage for significant interaction between algebra and topology, leading 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. The 2nd edition contains many more cohomology calculations for the sporadic groups, obtained by the authors and 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. |
| Additional Information |
| BISAC Categories: - Mathematics | Group Theory - Mathematics | Topology - General - Mathematics | Algebra - General |
| Dewey: 512.23 |
| LCCN: 2003064917 |
| Series: Grundlehren Der Mathematischen Wissenschaften |
| Physical Information: 0.81" H x 6.14" W x 9.21" (1.44 lbs) 324 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: Some Historical Background This book deals with the cohomology of groups, particularly finite ones. Historically, the subject has been one of significant interaction between algebra and topology and has directly led to the creation of such important areas of mathematics as homo- logical algebra and algebraic K-theory. It arose primarily in the 1920's and 1930's independently in number theory and topology. In topology the main focus was on the work ofH. Hopf, but B. Eckmann, S. Eilenberg, and S. MacLane (among others) made significant contributions. The main thrust of the early work here was to try to understand the meanings of the low dimensional homology groups of a space X. For example, if the universal cover of X was three connected, it was known that H2(X; A. ) depends only on the fundamental group of X. Group cohomology initially appeared to explain this dependence. In number theory, group cohomology arose as a natural device for describing the main theorems of class field theory and, in particular, for describing and analyzing the Brauer group of a field. It also arose naturally in the study of group extensions, N |