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arXiv:1901.04774 [math.GR]AbstractReferencesReviewsResources

Profinite groups with restricted centralizers of commutators

E. Detomi, M. Morigi, P. Shumyatsky

Published 2019-01-15Version 1

A group G has restricted centralizers if for each g in G the centralizer C_G(g) either is finite or has finite index in G. A theorem of Shalev states that a profinite group with restricted centralizers is abelian-by-finite. In the present article we handle profinite groups with restricted centralizers of word-values. We show that if w is a multilinear commutator word and G a profinite group with restricted centralizers of w-values, then the verbal subgroup w(G) is abelian-by-finite.

Categories: math.GR
Subjects: 20F24, 20E18, 20F12
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