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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Editorial Reviews
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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)
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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 Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
category stmod, extraspecial group, cohoniology ring, oil homology, degree one elements, stratification theorem, cohomology calculations, periodic module, projective resolution, subgroup complexes, bar resolution, spectral sequence, elementary abelian subgroup, cohomology ring, cellular chain complex, projective cover, rank variety, chain maps, krull dimension, identity neap, trivial module, projective module, associated primes, exact complex, free module Key Phrases - Capitalized Phrases (CAPs): (learn more)
Tensor Product Theorem, Duflot's Theorem, Serre's Theorem, Universal Coefficient Theorem New!
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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 Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
category stmod, extraspecial group, cohoniology ring, oil homology, degree one elements, stratification theorem, cohomology calculations, periodic module, projective resolution, subgroup complexes, bar resolution, spectral sequence, elementary abelian subgroup, cohomology ring, cellular chain complex, projective cover, rank variety, chain maps, krull dimension, identity neap, trivial module, projective module, associated primes, exact complex, free module Key Phrases - Capitalized Phrases (CAPs): (learn more)
Tensor Product Theorem, Duflot's Theorem, Serre's Theorem, Universal Coefficient Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 6
books:
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- An Introduction to Group Rings (Algebra and Applications) by César Polcino Milies in Back Matter
- Finite Groups (AMS Chelsea Publishing) by Daniel Gorenstein in Back Matter
- Modules and Group Algebras (Lectures in Mathematics. ETH Zürich) by Jon F. Carlson in Back Matter
- Science and Technology: A Five Year Outlook by Acd Sci Nat in Front Matter
- Representations and Cohomology: Volume 2, Cohomology of Groups and Modules (Cambridge Studies in Advanced Mathematics) by D. J. Benson in Back Matter
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