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On profinite groups in which centralizers have bounded rank

Pavel Shumyatsky

Department of Mathematics, University of Brasilia, Brazil

https://doi.org/10.1142/S0219199722500559Cited by:2 (Source: Crossref)

Abstract

The paper deals with profinite groups in which centralizers are of finite rank. For a positive integer $r$ $r$ we prove that if $G$ $G$ is a profinite group in which the centralizer of every nontrivial element has rank at most $r$ $r$ , then $G$ $G$ is either a pro- $p$ $p$ group or a group of finite rank. Further, if $G$ $G$ is not virtually a pro- $p$ $p$ group, then $G$ $G$ is virtually of rank at most $r + 1$ $r + 1$ .

Keywords:

AMSC: 20E18

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