On verbal subgroups in finite and profinite groups

Abstract

Let $w$ be a multilinear commutator word. In the present paper we describe recent results that show that if $G$ is a profinite group in which all $w$-values are contained in a union of finitely (or in some cases countably) many subgroups with a prescribed property, then the verbal subgroup $w(G)$ has the same property as well. In particular, we show this in the case where the subgroups are periodic or of finite rank.

arXiv admin note: substantial text overlap with arXiv:1112.5879

References in corpus (1)

• On profinite groups in which commutators are covered by finitely many subgroups