Profinite groups in which centralizers are virtually procyclic
Group Theory
2019-10-14 v1
Abstract
The article deals with profinite groups in which centralizers are virtually procyclic. Suppose that G is a profinite group such that the centralizer of every nontrivial element is virtually torsion-free while the centralizer of every element of infinite order is virtually procyclic. We show that G is either virtually pro-p for some prime p or virtually torsion-free procyclic. The same conclusion holds for profinite groups in which the centralizer of every nontrivial element is virtually procyclic; moreover, if G is not pro-p, then G has finite rank.
Keywords
Cite
@article{arxiv.1910.04838,
title = {Profinite groups in which centralizers are virtually procyclic},
author = {Pavel Shumyatsky and Pavel Zalesskii},
journal= {arXiv preprint arXiv:1910.04838},
year = {2019}
}