Profinite groups in which centralizers are virtually procyclic

[摘要] 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 (Theorem 1. 1). The same conclusion holds for profinite groups in which the centralizer of every nontrivial element is virtually procyclic (Theorem 1.2); moreover, if G is not pro-p, then G has finite rank. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-11-15

[关键词] Profinite groups;Procyclic groups;Centralizers