Profinite groups with pronilpotent centralizers

TL;DR

This paper studies profinite groups with pronilpotent centralizers, proving they are virtually pronilpotent and detailing the structure of their finite quotients.

Contribution

It establishes that profinite CN-groups have an open maximal normal pronilpotent subgroup and characterizes their finite quotients, advancing understanding of their structure.

Findings

F is open in G

G/F is finite and structurally described

Profinite CN-groups are virtually pronilpotent

Abstract

The article deals with profinite groups in which the centralizers are pronilpotent (CN-groups). It is shown that such groups are virtually pronilpotent. More precisely, let G be a profinite CN-group, and let F be the maximal normal pronilpotent subgroup of G. It is shown that F is open and the structure of the finite quotient G/F is described in detail.