2023/11/09 by Marco Fusari, Fusari, Marco, Andrea Previtali +3 · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Advanced Topology and Set Theory #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2311.05575
openalex publication_date 2023/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a permutation group G, the derangement graph of G is the Cayley graph with connection set the derangements of G. The group G is said to be innately transitive if G has a transitive minimal normal subgroup. Clearly, every primitive group is innately transitive. We show that, besides an infinite family of explicit exceptions, there exists a function f:ℕ→ ℕ such that, if G is innately transitive of degree n and the derangement graph of G has no clique of size k, then n≤ f(k). Motivation for this work arises from investigations on Erdős-Ko-Rado type theorems for permutation groups.