On the EKR-module property

In recent years, the generalization of the Erdős–Ko–Rado (EKR) theorem to permutation groups has been of much interest. A transitive group is said to satisfy the EKR-module property if the characteristic vector of every maximum intersecting set is a linear combination of the characteristic vectors of cosets of stabilizers of points. This generalization of the well-known permutation group version of the Erdős–Ko–Rado (EKR) theorem was introduced by K. Meagher in 28. In this article, we present several infinite families of permutation groups satisfying the EKR-module property, which shows that permutation groups satisfying this property are quite diverse.