Profinite groups with restricted centralizers of commutators
Group Theory
2019-01-16 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1901.04774,
title = {Profinite groups with restricted centralizers of commutators},
author = {E. Detomi and M. Morigi and P. Shumyatsky},
journal= {arXiv preprint arXiv:1901.04774},
year = {2019}
}