Pavel Shumyatsky, Pavel Zalesskii
Published 2019-10-10Version 1
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.
On profinite groups in which centralizers have bounded rank
Profinite groups with a cyclotomic $p$-orientation
Procyclic coverings of commutators in profinite groups
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