A Modification of the Schreier-Sims Algorithm Utilising the Transitivity of the Stabiliser Subgroups

A modification of the Schreier-Sims algorithm is described which builds a permutation group utilising the transitivity of the stabiliser subgroups. Alternating and symmetric groups are recognised by their transitivity, resulting in a greatly improved time to build symmetric and alternating groups.
The algorithm has applications to graph isomorphism and other combinatorial isomorphism algorithms, as well as permutation group algorithms.