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Algebra and Discrete Mathematics, 2012, Volume 14, Issue 1, Pages 1–13
(Mi adm80)
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This article is cited in 5 scientific papers (total 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.
Received: 17.04.2012 Revised: 20.05.2012
Citation:
Cristina Acciarri, Pavel Shumyatsky, “On verbal subgroups in finite and profinite groups”, Algebra Discrete Math., 14:1 (2012), 1–13
Linking options:
https://www.mathnet.ru/eng/adm80 https://www.mathnet.ru/eng/adm/v14/i1/p1
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