Profinite groups with many elements with large nilpotentizer and generalizations

Martino Garonzi; Andrea Lucchini; Nowras Otmen

Profinite groups with many elements with large nilpotentizer and generalizations

Group Theory 2025-05-23 v1

Authors: Martino Garonzi , Andrea Lucchini , Nowras Otmen

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 $G$ .

Keywords

finite group theory algebraic group actions group theory

Cite

@article{arxiv.2505.16589,
  title  = {Profinite groups with many elements with large nilpotentizer and generalizations},
  author = {Martino Garonzi and Andrea Lucchini and Nowras Otmen},
  journal= {arXiv preprint arXiv:2505.16589},
  year   = {2025}
}

Profinite groups with many elements with large nilpotentizer and generalizations

Abstract

Keywords

Cite

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