An Erd\H{o}s-Ko-Rado theorem for finite 2-transitive groups

TL;DR

This paper extends the Erd ext{"o}s-Ko-Rado theorem to finite 2-transitive groups, characterizing the maximum size of intersecting sets of permutations and unifying previous results.

Contribution

It provides a new general proof for the maximum size of intersecting sets in finite 2-transitive groups, generalizing prior specific cases.

Findings

Maximum intersecting set size is |G|/|X| in finite 2-transitive groups

Unifies previous results on intersecting permutations

Offers a new proof technique for Erd ext{"o}s-Ko-Rado type theorems

Abstract

We prove an analogue of the classical Erd\H{o}s-Ko-Rado theorem for intersecting sets of permutations in finite 2-transitive groups. Given a finite group G acting faithfully and 2-transitively on the set X, we show that an intersecting set of maximal size in G has cardinality |G|/|X|. This generalises and gives a unifying proof of some similar recent results in the literature.