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

Let G be a finite 2-group of maximal nilpotency class, and let BG be its classifying space. We prove that iteratedMassey products in H*(BG; F2) 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. © 2012 American Mathematical Society.