On profinite groups with word values covered by nilpotent subgroups |
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Authors: | Eloisa Detomi Marta Morigi Pavel Shumyatsky |
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Institution: | 1.Dipartimento di Matematica,Università di Padova,Padova,Italy;2.Dipartimento di Matematica,Università di Bologna,Bologna,Italy;3.Department of Mathematics,University of Brasilia,Brasilia-DF,Brazil |
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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]. |
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