Compact $p$-adic analytic groups in which centralizers are abelian

Luis Mendonça; Thomas S. Weigel; Theo Zapata

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arXiv · 2411.03880

Compact $p$-adic analytic groups in which centralizers are abelian

Luis Mendonça·Thomas S. Weigel·Theo Zapata

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Abstract

Using methods of associative algebras, Lie theory, group cohomology, and modular representation theory, we construct profinite $p$-adic analytic groups such that the centralizer of each of their non-trivial elements is abelian. The paper answers questions of P.~Shumyatsky, P.~Zalesskii, and T.~Zapata in the Israel J. Math., v.~230, 2019.

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Luis Mendonça, Thomas S. Weigel, Theo Zapata. 2024-11-06. Compact $p$-adic analytic groups in which centralizers are abelian. https://arxiv.org/abs/2411.03880

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