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arXiv · 2505.16589

Profinite groups with many elements with large nilpotentizer and generalizations

Martino Garonzi·Andrea Lucchini·Nowras Otmen
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Abstract

Given a profinite group $G$ and a family $\mathcal{F}$ of finite groups closed under taking subgroups, direct products and quotients, denote by $\mathcal{F}(G)$ the set of elements $g \in G$ such that $\{x \in G\ |\ \langle g,x \rangle \ \mbox{is a pro-}\mathcal{F} \mbox{ group}\}$ has positive Haar measure. We investigate the properties of $\mathcal{F}(G)$ for various choices of $\mathcal{F}$ and its influence on the structure of $G$.

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Martino Garonzi, Andrea Lucchini, Nowras Otmen. 2025-05-22. Profinite groups with many elements with large nilpotentizer and generalizations. https://arxiv.org/abs/2505.16589

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