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arXiv · 1910.04838

Profinite groups in which centralizers are virtually procyclic

Pavel Shumyatsky·Pavel Zalesskii
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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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BibTeXRIS

Pavel Shumyatsky, Pavel Zalesskii. 2019-10-10. Profinite groups in which centralizers are virtually procyclic. https://arxiv.org/abs/1910.04838

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