Year: 2026
Type: preprint
Abstract: Let $G$ be a finite group and let $\mathrm{P}_{\mathcal{U}}(G)$ denote the probability that two randomly chosen elements of $G$ generate a supersoluble subgroup. We prove that if $\mathrm{P}_{\mathcal{U}}(G) > 16/25$ then $G$ is supersoluble, and that the bound $16/25$ is sharp, being attained by the group $G = (C_5 \times C_5) \rtimes Q_8$, where $Q_8$ acts faithfully and irreducibly on $C_5 \times C_5$.
Source: arXiv (Cornell University)
Author: Lucchini, Andrea
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7167898871