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Titlebook: Cohomology of Groups; Kenneth S. Brown Textbook 1982 Springer-Verlag New York Inc. 1982 Abelian group.Cohomology.Groups.Gruppe (Math.).Koh

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书目名称Cohomology of Groups
编辑Kenneth S. Brown
视频video
丛书名称Graduate Texts in Mathematics
图书封面Titlebook: Cohomology of Groups;  Kenneth S. Brown Textbook 1982 Springer-Verlag New York Inc. 1982 Abelian group.Cohomology.Groups.Gruppe (Math.).Koh
描述As a second year graduate textbook, .Cohomology of Groups. introduces students to cohomology theory (involving a rich interplay between algebra and topology) with a minimum of prerequisites. No homological algebra is assumed beyond what is normally learned in a first course in algebraic topology. The basics of the subject are given (along with exercises) before the author discusses more specialized topics.
出版日期Textbook 1982
关键词Abelian group; Cohomology; Groups; Gruppe (Math; ); Kohomologie
版次1
doihttps://doi.org/10.1007/978-1-4684-9327-6
isbn_ebook978-1-4684-9327-6Series ISSN 0072-5285 Series E-ISSN 2197-5612
issn_series 0072-5285
copyrightSpringer-Verlag New York Inc. 1982
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Cohomology Theory of Finite Groups, .-modules (namely, the induced modules . ⊗ .) with the following properties: (a) Every . ∈ . is acyclic for both homology and cohomology. (b) For every .-module . there is a module . ∈ . such that . is a quotient of . and . can be embedded in ..
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Textbook 1982pology) with a minimum of prerequisites. No homological algebra is assumed beyond what is normally learned in a first course in algebraic topology. The basics of the subject are given (along with exercises) before the author discusses more specialized topics.
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Some Homological Algebra,ed algebraic topology. The reader is advised to skip this section (or skim it lightly) and refer back to it as necessary. We will omit some of the proofs; these are either easy or else can be found in standard texts, such as Dold [1972], Spanier [1966], or MacLane [1963].
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Products,.′. Note that if . is projective over . and .′ is projective over .′ then . ⊗ .′ is projective over .[. × .′]. In fact, it suffices to verify this in the case where . = . and .′ = .′, in which case the assertion follows from the obvious isomorphism . ⊗ .′ ≈ .[. × .′].
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Finiteness Conditions,take the topological point of view, then we can compute .(.) and .*(., .) in terms of an arbitrary K(G, 1)-complex .. Since we have this freedom of choice, it is reasonable to try to choose . (or . to be as “small” as possible, and this leads to various finiteness conditions on ..
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