Intersection of Conjugate Solvable Subgroups in Symmetric Groups

Abstract

It is proved that for any solvable subgroup G of an almost simple group S with simple socle isomorphic to An, n ≥ 5, there are elements x, y, z, t ∈ S such that G ∩ G^x ∩ G^y ∩ G^z ∩ G^t = 1.