Titlebook: Cohomology Rings of Finite Groups; With an Appendix: Ca Jon F. Carlson,Lisa Townsley,Mucheng Zhang Book 2003 Springer Science+Business Medi

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Document Sentiment Classification,In this chapter, we begin to concentrate on cohomology of groups, frequently with focus on finite groups. From an algebraic viewpoint, group cohomology is a component of the extension theory of modules over the group algebra .. Let . be any commutative ring of coefficients and . a .-module.

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Group Algebras,Let . be a finite group and let . be a field, or perhaps just a ring with unity.

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Projective Resolutions,In this chapter, we begin to concentrate on cohomology of groups, frequently with focus on finite groups. From an algebraic viewpoint, group cohomology is a component of the extension theory of modules over the group algebra .. Let . be any commutative ring of coefficients and . a .-module.

cauda-equina

Varieties and Elementary Abelian Subgroups,The aim of this chapter is to develop and prove a generalized version of Quillen’s Dimension Theorem [122, 125]. Our main theorem says that every .-module is a direct summand of a module that has a filtration in which the factors are induced from elementary abelian subgroups. Quillen’s theorem is one of the several consequences that we explore.

subordinate

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Cohomology Rings of Modules, ring H* (., .) via the isomorphism ., and the fact that Hom.(., .) is a finitely generated .-module. For this reason there exists a cohomological support variety ..(.) of the module . which is a subvariety of ..(.) and which reflects many of the homological properties of the module.

fatuity

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Document Sentiment Classification,not pretend that the material is exhaustive or evenhanded; rather we emphasize the aspects of the subject that have direct application in later chapters. We assume basic knowledge of groups, rings, modules and homomorphisms as found in a standard first year graduate algebra course.

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