Cohomological uniqueness, Massey products and the modular isomorphism problem for 2-groups of maximal nilpotency class

Ruiz, Albert; Viruel, Antonio

doi:10.1090/S0002-9947-2013-05756-X

Cohomological uniqueness, Massey products and the modular isomorphism problem for $2$-groups of maximal nilpotency class
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by Albert Ruiz and Antonio Viruel PDF

Trans. Amer. Math. Soc. 365 (2013), 3729-3751 Request permission

Abstract:

Let $G$ be a finite $2$-group of maximal nilpotency class, and let $BG$ be its classifying space. We prove that iterated Massey products in $H^*(BG;\mathbb {F}_2)$ do characterize the homotopy type of $BG$ among $2$-complete spaces with the same cohomological structure. As a consequence we get an alternative proof of the modular isomorphism problem for $2$-groups of maximal nilpotency class.

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