A note on strong conciseness in virtually nilpotent profinite groups

Abstract

A group word w is said to be strongly concise in a class $${\mathcal {C}}$$ C of profinite groups if, for every group G in $${\mathcal {C}}$$ C such that w takes less than $$2^{\aleph _0}$$ 2 ℵ 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.