A group G has restricted centralizers if for each g in G the centralizer 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 paper 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.
Profinite groups with restricted centralizers of commutators / Detomi E.; Morigi M.; Shumyatsky P.. - In: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS. - ISSN 0308-2105. - STAMPA. - 150:5(2020), pp. 2301-2321. [10.1017/prm.2019.17]
Profinite groups with restricted centralizers of commutators
Morigi M.;
2020
Abstract
A group G has restricted centralizers if for each g in G the centralizer 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 paper 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.| File | Dimensione | Formato | |
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