The Erdős-Ko-Rado property for some 2-transitive groups

2013/08/02 by Bahman Ahmadi, Ahmadi, Bahman, Karen Meagher +1
Computer Science · Mathematics · #05C35 #05C69 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1308.0621

openalex publication_date 2013/08/02 · openalex created_date 2022/09/04 · openalex updated_date 2026/07/28

Abstract

A subset of a group G of Sym(n) is intersecting if for any pair of permutations π,σ∈ G there is an i in 1,2,...,n such that π(i) = σ(i). It has been shown, using an algebraic approach, that the largest intersecting sets in each of Sym(n), Alt(n) and PGL(2,q) are exactly the cosets of the point-stabilizers. In this paper, we show how this method can be applied more generally to many 2-transitive groups. We then apply this method to the Mathieu groups and to all 2-transtive groups with degree no more than 20.

Citations

• Maximum Intersecting Families of Permutations

Related

• Erd\Hos-Ko-Rado problems for permutation groups
• The Erdős-Ko-Rado property for some permutation groups
• An Erd\Hos-Ko-Rado theorem for finite 2-transitive groups
• Intersection density of transitive groups with cyclic point stabilizers
• A new proof of the Erdős-Ko-Rado theorem for intersecting families of permutations