Profinite groups with many elements with large nilpotentizer and generalizations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908374451355648 |
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| author | Garonzi, Martino Lucchini, Andrea Otmen, Nowras |
| author_facet | Garonzi, Martino Lucchini, Andrea Otmen, Nowras |
| contents | 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 $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16589 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Profinite groups with many elements with large nilpotentizer and generalizations Garonzi, Martino Lucchini, Andrea Otmen, Nowras Group Theory 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 $G$. |
| title | Profinite groups with many elements with large nilpotentizer and generalizations |
| topic | Group Theory |
| url | https://arxiv.org/abs/2505.16589 |