All 2-transitive groups have the EKR-module property. (English) Zbl 1448.05228
Summary: 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.
MSC:
| 05E18 | Group actions on combinatorial structures |
| 05D05 | Extremal set theory |
| 05C69 | Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) |
| 05A05 | Permutations, words, matrices |
| 20B30 | Symmetric groups |
Software:
OEISReferences:
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