Let N stand for the class of nilpotent groups or one of its well-known generalizations. For a multilinear commutator word w and a profinite group G we show that w(G) is finite-by-N if and only if the set of wvalues in G is covered by countably many finite-by-N subgroups. Earlier this was known only in the case where w = x or w = [x, y].

On profinite groups with word values covered by nilpotent subgroups

Morigi, Marta;
2018

Abstract

Let N stand for the class of nilpotent groups or one of its well-known generalizations. For a multilinear commutator word w and a profinite group G we show that w(G) is finite-by-N if and only if the set of wvalues in G is covered by countably many finite-by-N subgroups. Earlier this was known only in the case where w = x or w = [x, y].
2018
Detomi, Eloisa; Morigi, Marta; Shumyatsky, Pavel
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/653790
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