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
On verbal subgroups in finite and profinite groups / Acciarri, C; Shumyatsky, P.. - In: ALGEBRA AND DISCRETE MATHEMATICS. - ISSN 1726-3255. - 14:1(2012), pp. 1-13.
On verbal subgroups in finite and profinite groups
Acciarri C;
2012
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
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