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 W 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 Erdos–Ko–Rado type theorems for permutation groups.

Cliques in derangement graphs for innately transitive groups

Previtali A.
Co-primo
;
Spiga P.
Co-primo
2024

Abstract

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 W 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 Erdos–Ko–Rado type theorems for permutation groups.
Articolo in rivista - Articolo scientifico
primitive groups
English
15-mar-2024
2024
none
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/481962
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