We prove the following results. Let to be a multilinear commutator word. If G is a profinite group in which all w-values are contained in a union of countably many periodic subgroups, then the verbal subgroup w(G) is locally finite. If G is a profinite group in which all w-values are contained in a union of countably many subgroups of finite rank, then the verbal subgroup w(G) has finite rank as well. As a by-product of the techniques developed in the paper we also prove that if G is a virtually soluble profinite group in which all to-values have finite order, then w(G) is locally finite and has finite exponent.

On countable coverings of word values in profinite groups

MORIGI, MARTA;
2015

Abstract

We prove the following results. Let to be a multilinear commutator word. If G is a profinite group in which all w-values are contained in a union of countably many periodic subgroups, then the verbal subgroup w(G) is locally finite. If G is a profinite group in which all w-values are contained in a union of countably many subgroups of finite rank, then the verbal subgroup w(G) has finite rank as well. As a by-product of the techniques developed in the paper we also prove that if G is a virtually soluble profinite group in which all to-values have finite order, then w(G) is locally finite and has finite exponent.
2015
Eloisa Detomi;Marta Morigi;Pavel Shumyatsky
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/404159
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