2019/11/25 by Meagher, Karen, Sin, Peter · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics #Primary 05C35 #Secondary 05C69
paper · doi:10.48550/arxiv.1911.11252
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 group. Specifically, the characteristic vector of any maximum intersecting set in a 2-transitive group is the linear combination of the characteristic vectors of the stabilizers of a points and their cosets. We also consider when the derangement graph of a 2-transitive group is connected and when a maximum intersecting set is a subgroup or a coset of a subgroup.