This article is cited in 5 papers

RESEARCH ARTICLE

On verbal subgroups in finite and profinite groups

Cristina Acciarri, Pavel Shumyatsky

Department of Mathematics, University of Brasilia, Brasilia-DF, 70910-900 Brazil

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.

Keywords: Profinite groups, verbal subgroups, coverings, multilinear commutators.

MSC: Primary 20E18; Secondary 20F14

Received: 17.04.2012
Revised: 20.05.2012

Language: English

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