Compact groups with a set of positive Haar measure satisfying a nilpotent law

Abstract

The following question is proposed by Martino, Tointon, Valiunas and Ventura in [4, question 1·20]: Let G be a compact group, and suppose that Nk(G) = {(x1, ... , xk+1) ∈ Gk+1| [x1, ... , xk+1] = 1} has positive Haar measure in. Does G have an open k-step nilpotent subgroup? We give a positive answer for. © The Author(s), 2021. Published by Cambridge University Press on behalf of Cambridge Philosophical Society.