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.File | Dimensione | Formato | |
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