A permutation group G of a finite set acts componentwise on the Cartesian square ². The largest subgroup of Sym () that has the same orbits on ² as G is called the 2 -closure of G. The rank of G is the number of its orbits on ². If the rank of G is 3 and the order is even, then an undirected graph with vertex set is defined, up to taking the complement, for which one of the two non-diagonal orbits of G on ² is taken as the edge set. Such a graph is called a rank 3 graph. The full automorphism group of this graph coincides with the 2 -closure of G and contains G as a subgroup. At present, with the exception of the case when G is an almost simple group, there exists an explicit description of the 2 -closures of rank 3 groups G. In this paper, we fill the existing gap, thereby completing the description of the automorphism groups of rank 3 graphs.
Wang et al. (Fri,) studied this question.