Two-closure of supersolvable permutation group in polynomial time

Abstract

The 2-closure G of a permutation group G on Ω is defined to be the largest permutation group on Ω, having the same orbits on Ω × Ω as G. It is proved that if G is supersolvable, then G can be found in polynomial time in |Ω|. As a byproduct of our technique, it is shown that the composition factors of G are cyclic or alternating.