A note on strong conciseness in virtually nilpotent profinite groups

Abstract

A group word w is said to be strongly concise in a class {mathcal {C}} of profinite groups if, for every group G in {mathcal {C}} such that w takes less than 2^{aleph _0} values in G, the verbal subgroup w(G) is finite. In this paper, we prove that every group word is strongly concise in the class of virtually nilpotent profinite groups.