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.

Fusari, M., Previtali, A., Spiga, P. (2024). Cliques in derangement graphs for innately transitive groups. JOURNAL OF GROUP THEORY, 27(5), 929-965 [10.1515/jgth-2023-0284].

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
27
5
929
965
partially_open
Fusari, M., Previtali, A., Spiga, P. (2024). Cliques in derangement graphs for innately transitive groups. JOURNAL OF GROUP THEORY, 27(5), 929-965 [10.1515/jgth-2023-0284].
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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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