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arXiv · 2405.20964

Profinite groups with soluble centralisers

Pavel Shumyatsky·Anitha Thillaisundaram
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Abstract

We show that a profinite group, in which the centralisers of non-trivial elements are metabelian, is either virtually pro-$p$ or virtually soluble of derived length at most 4. We furthermore show that a prosoluble group, in which the centralisers of non-trivial elements are soluble of bounded derived length, is either soluble or virtually pro-$p$.

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Pavel Shumyatsky, Anitha Thillaisundaram. 2024-05-31. Profinite groups with soluble centralisers. https://arxiv.org/abs/2405.20964

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