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

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 $H^*(BG;\F_2)$ 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.

References in corpus (1)

• The modular isomorphism problem for finite $p$-groups with a cyclic subgroup of index $p^2$

Cited by in corpus (3)

• The Modular Isomorphism Problem: a survey
• A-infinity structures and Massey products
• Abelian invariants and a reduction theorem for the modular isomorphism problem