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 a linear combination of the characteristic vectors of the stabilizers of 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.

中文翻译：

---

所有2个传递组均具有EKR-module属性

我们证明每个2及物组都有一个称为EKR-module属性的属性。此属性表示组中排列的最大相交集的特征。具体地，在两个及物组中的任何最大相交集的特征向量是点的稳定子及其同集的特征向量的线性组合。我们还考虑了何时连接两个及物组的重排图，以及何时最大相交集是子组或子组的陪集。