Intersection density of transitive groups of certain degrees

Abstract

Two elements $g$ and $h$ of a permutation group $G$ acting on a set $V$ are said to be intersecting if $g(v)=h(v)$ for some $v\in V$. More generally, a subset $\mathcal{F}$ of $G$ is an intersecting set if every pair of elements of $\mathcal{F}$ is intersecting. The intersection density $\rho (G)$ of a transitive permutation group $G$ is the maximum value of the quotient $|\mathcal{F}|/|G_v|$ where $\mathcal{F}$ runs over all intersecting sets in $G$ and $G_v$ is a stabilizer of $v\in V$. In this paper the intersection density of transitive groups of degree twice a prime is determined, and proved to be either $1$ or $2$. In addition, it is proved that the intersection density of transitive groups of prime power degree is $1$.

10 pages

Cited by in corpus (1)

• On intersection density of transitive groups of degree a product of two odd primes