All $2$-transitive groups have the EKR-module property
Combinatorics
2022-07-13 v3
Abstract
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.
Cite
@article{arxiv.1911.11252,
title = {All $2$-transitive groups have the EKR-module property},
author = {Karen Meagher and Peter Sin},
journal= {arXiv preprint arXiv:1911.11252},
year = {2022}
}
Comments
17 pages. Some edits made for better clarity