We prove an analogue of the classical Erdos-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 Ω, we show that an intersecting set of maximal size in G has cardinality |G|/|Ω|. This generalises and gives a unifying proof of some similar recent results in the literature.
Meagher, K., Spiga, P., Tiep, P. (2016). An Erdos-Ko-Rado theorem for finite 2-transitive groups. EUROPEAN JOURNAL OF COMBINATORICS, 55, 100-118 [10.1016/j.ejc.2016.02.005].
An Erdos-Ko-Rado theorem for finite 2-transitive groups
SPIGA, PABLOSecondo
;
2016
Abstract
We prove an analogue of the classical Erdos-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 Ω, we show that an intersecting set of maximal size in G has cardinality |G|/|Ω|. This generalises and gives a unifying proof of some similar recent results in the literature.
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