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

Abstract

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