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].
Detomi, E., Morigi, M., Shumyatsky, P. (2018). On profinite groups with word values covered by nilpotent subgroups. ISRAEL JOURNAL OF MATHEMATICS, 226(2), 993-1008 [10.1007/s11856-018-1720-2].
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].File in questo prodotto:
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