Abstract
A subset S of a group G ≤ Sym(n) is intersecting if for any pair of permutations \({\pi, \sigma \in S}\) there is an \({i \in {1, 2, . . . , n}}\) such that \({\pi (i) = \sigma (i)}\). 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 approach can be applied more generally to many 2-transitive groups. We then apply this method to the Mathieu groups and to all 2-transitive groups with degree no more than 20.
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Research supported by NSERC.
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Ahmadi, B., Meagher, K. The Erdős-Ko-Rado Property for Some 2-Transitive Groups. Ann. Comb. 19, 621–640 (2015). https://doi.org/10.1007/s00026-015-0285-6
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DOI: https://doi.org/10.1007/s00026-015-0285-6