On countable coverings of word values in profinite groups
Group Theory
2013-09-04 v1
Abstract
We prove the following results. Let w 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 w-values have finite order, then w(G) is locally finite and has finite exponent.
Keywords
Cite
@article{arxiv.1309.0636,
title = {On countable coverings of word values in profinite groups},
author = {Eloisa Detomi and Marta Morigi and Pavel Shumyatsky},
journal= {arXiv preprint arXiv:1309.0636},
year = {2013}
}