English

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.

Keywords

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

R2 v1 2026-06-23T02:53:01.465Z