Control of fusion and cohomology of trivial source modules

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• Let G be a finite group and H a subgroup. We give an algebraic proof of Mislin's theorem which states that the restriction map from G to H on mod-p cohomology is an isomorphism if and only if H controls p-fusion in G. We follow the approach of P. Symonds [P. Symonds, Mackey functors and control of fusion, Bull. London Math. Soc. 36 (2004) 623?632] and consider the cohomology of trivial source modules.

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