Profinite groups in which centralizers are virtually procyclic
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Publication:6326968
DOI10.1016/J.JALGEBRA.2021.07.008arXiv1910.04838MaRDI QIDQ6326968
Pavel Shumyatsky, Pavel Zalesskij
Publication date: 10 October 2019
Abstract: 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.
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