On profinite groups in which centralizers have bounded rank
Group Theory
2022-07-19 v3
Abstract
For a positive integer r we prove that if G is a profinite group in which the centralizer of every nontrivial element has rank at most r, then G is either a pro-p group or a group of finite rank. Further, if G is not virtually a pro-p group, then G is virtually of rank at most r+1.
Keywords
Cite
@article{arxiv.2004.05977,
title = {On profinite groups in which centralizers have bounded rank},
author = {Pavel Shumyatsky},
journal= {arXiv preprint arXiv:2004.05977},
year = {2022}
}
Comments
Following a referee's suggestions some changes implemented. The paper is much shorter now. Will be published in Communications in Contemporary Mathematics