Two-closure of rank 3 groups in polynomial time

Abstract

A finite permutation group G on Ω is a rank 3 group if it has precisely three orbits in its induced action on Ω×Ω. The largest permutation group on Ω having the same orbits as G on Ω×Ω is the 2-closure of G. We construct a polynomial-time algorithm which, given generators of a rank 3 group, computes generators of its 2-closure.