Profinite groups in which centralizers are abelian
Group Theory
2018-07-09 v1
Abstract
The article deals with profinite groups in which the centralizers are abelian (CA-groups), that is, with profinite commutativity-transitive groups. It is shown that such groups are virtually pronilpotent. More precisely, let G be a profinite CA-group. It is shown that G has a normal open subgroup N which is either abelian or pro-p. Further, a rather detailed information about the finite quotient G/N is obtained.
Cite
@article{arxiv.1807.02429,
title = {Profinite groups in which centralizers are abelian},
author = {Pavel Shumyatsky and Pavel Zalesskii and Theo Zapata},
journal= {arXiv preprint arXiv:1807.02429},
year = {2018}
}
Comments
20 pages