Given a permutation group G, the derangement graph Γ G of G is the Cayley graph with
connection set the set of all derangements of G. We prove that, when G is transitive of …

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 …

We prove that every 2-transitive group has a property called the EKR-module property. This
property gives a characterization of the maximum intersecting sets of permutations in the …

Given a finite transitive permutation group $ G\leq\operatorname {Sym}(\Omega) $, with
$|\Omega|\geq 2$, the derangement graph $\Gamma_G $ of $ G $ is the Cayley graph …

Consider a group $ G $ acting on a set $\Omega $, the vector $ v_ {a, b} $ is a vector with
the entries indexed by the elements of $ G $, and the $ g $-entry is 1 if $ g $ maps $ a $ to …

A subset Y of the general linear group is called t-intersecting if for all, or equivalently x and y
agree pointwise on a t-dimensional subspace of for all. We show that, if n is sufficiently large …

In this paper, we show that both the general linear group GL (2, q) and the special linear
group SL (2, q) have both the EKR property and the EKR-module property. This is done …

A subset F of a finite transitive group G≤ Sym (Ω) is intersecting if for any g, h∈ F there
exists ω∈ Ω such that ω g= ω h. The intersection density ρ (G) of G is the maximum of {| F|| G …

A subset F of a finite transitive group G≤ Sym (Ω) is intersecting if any two elements of F
agree on an element of Ω. The intersection density of G is the number ρ (G)= max⁡{| F|/| G …

The intersection density of a finite transitive group G≤ Sym (Ω) is the rational number ρ (G)
given by the ratio between the maximum size of a subset of G in which any two permutations …