Cliques in derangement graphs for innately transitive groups
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866917647835201536 |
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| author | Fusari, Marco Previtali, Andrea Spiga, Pablo |
| author_facet | Fusari, Marco Previtali, Andrea Spiga, Pablo |
| contents | 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 $f:\mathbb{N}\to \mathbb{N}$ such that, if $G$ is innately transitive of degree $n$ and the derangement graph of $G$ has no clique of size $k$, then $n\le f(k)$.
Motivation for this work arises from investigations on Erdős-Ko-Rado type theorems for permutation groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_05575 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cliques in derangement graphs for innately transitive groups Fusari, Marco Previtali, Andrea Spiga, Pablo Group Theory Number Theory 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 $f:\mathbb{N}\to \mathbb{N}$ such that, if $G$ is innately transitive of degree $n$ and the derangement graph of $G$ has no clique of size $k$, then $n\le f(k)$. Motivation for this work arises from investigations on Erdős-Ko-Rado type theorems for permutation groups. |
| title | Cliques in derangement graphs for innately transitive groups |
| topic | Group Theory Number Theory |
| url | https://arxiv.org/abs/2311.05575 |