A Reduction Algorithm for Large-Base Primitive Permutation Groups

The authors present a nearly linear-time Las Vegas algorithm that, given a large-base primitive permutation group, constructs its natural imprimitive representation. A large-base primitive permutation group is a subgroup of a wreath product of symmetric groups Sn and Sr in product action on r-tuples of k-element subsets of {1, ..., n}, containing Anr. The algorithm is a randomised speed-up of a deterministic algorithm of Babai, Luks, and Seress.