On profinite groups in which centralizers have bounded rank

2020/04/13 by Pavel Shumyatsky, Shumyatsky, Pavel
Engineering · Mathematics · #20E18 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings, Modules, and Algebras #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2004.05977

openalex publication_date 2020/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Profinite groups in which centralizers are virtually procyclic
• Profinite groups with pronilpotent centralizers
• Profinite groups in which many elements have prime power order
• Profinite groups with soluble centralisers
• Profinite groups with restricted centralizers of π-elements