Cohomological uniqueness of finite groups of prime power order
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Date
2024-05-31Author
Guerrero Sánchez, Lander
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Group cohomology originates, along with homological algebra, from algebraic topology and the study of cohomology groups of certain topological spaces. Given a finite group G, we can associate to it a classifying space BG, which satisfies that its first homotopy group is isomorphic to G, and its higher order homotopy groups are trivial. We can then define the cohomology groups Hn(G, V ) of G with coefficients on an RG-module V , where R is a commutative ring, to be the cohomology groups of its classifying space BG, see [Hat02]. It is also possible to give a purely algebraic definition of the cohomology groups of G in terms of derived functors, and in fact this is the approach that we will follow throughout this thesis.