Year: 2025
Type: article
Abstract: Given a profinite group G and a family $$\mathcal {F}$$ F of finite groups closed under taking subgroups, direct products and quotients, denote by $$\mathcal {F}(G)$$ F ( G ) the set of elements $$g \in G$$ g ∈ G such that $$\{x \in G\ |\ \langle g,x \rangle \ \text{ is } \text{ a } \text{ pro- }\mathcal {F} \text{ group }\}$$ { x ∈ G | ⟨ g , x ⟩ is a pro- F group } has positive Haar measure. We investigate the properties of $$\mathcal {F}(G)$$ F ( G ) for various choices of $$\mathcal {F}$$ F and the influence of $$\mathcal {F}(G)$$ F ( G ) on the structure of G when $$\mu (\mathcal F(G))>0$$ μ ( F ( G ) ) > 0 .
Source: Monatshefte für Mathematik
Authors: Martino Garonzi, Andrea Lucchini, Nowras Otmen
Institutions: University of Ferrara, University of Padua
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Awards: G5245466801, G7933988292, G972786147
OpenAlex ID: W4414598722