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- W4386876251 abstract "The emph{intersection density} of a finite transitive group $Gleq operatorname{Sym}(Omega)$ is the rational number $rho(G)$ given by the ratio between the maximum size of a subset of $G$ in which any two permutations agree on some elements of $Omega$ and the order of a point stabilizer of $G$. In 2022, Meagher asked whether $rho(G)in {1,frac{3}{2},3}$ for any transitive group $G$ of degree $3p$, where $pgeq 5$ is an odd prime. For the primitive case, it was proved in [emph{J. Combin. Ser. A}, 194:105707, 2023] that the intersection density is $1$. It is shown in this paper that the answer to this question is affirmative for non-quasiprimitive groups, unless possibly when $p = q+1$ is a Fermat prime and $Omega$ admits a unique $G$-invariant partition $mathcal{B}$ such that the induced action $overline{G}_mathcal{B}$ of $G$ on $mathcal{B}$ is an almost simple group containing $operatorname{PSL}_{2}(q)$." @default.
- W4386876251 created "2023-09-20" @default.
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- W4386876251 date "2023-09-18" @default.
- W4386876251 modified "2023-09-27" @default.
- W4386876251 title "The ErdH{o}s-Ko-Rado Theorem for non-quasiprimitive groups of degree $3p$" @default.
- W4386876251 doi "https://doi.org/10.48550/arxiv.2309.09906" @default.
- W4386876251 hasPublicationYear "2023" @default.
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