Year: 2026
Type: preprint
Abstract: Let $G$ be a finite group. The co-intersection graph $Δ_G ^c$ of $G$ has as its vertices the nontrivial proper subgroups of $G$, with edges joining those pairs of subgroups which intersect trivially. It is clear that every connected component of $Δ_G ^c$ has diameter at most three. In this Note, we show that when $T$ is a nonabelian finite simple group, $Δ_T$ is connected of diameter exactly two. We also make several observations about the extent to which a finite group is determined by its co-intersection graph, and about the class of finite graphs arising as co-intersection graphs.
Source: arXiv (Cornell University)
Authors: Bradford, Henry, Rekvényi, Kamilla
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Università degli Studi di Padova
OpenAlex ID: W7212003970