Fast management of permutation groups

Abstract

Novel algorithms for computation in permutation groups are presented. They provide an order-of-magnitude improvement in the worst-case analysis of the basic permutation-group problems, including membership testing and computing the order of the group. For deeper questions about the group, including finding composition factors, an improvement of up to four orders of magnitude is realized. These and other essential investigations are all accomplished in O(n/sup 4/log/sup c/n) time. The approach is distinguished by its recognition and use of the intrinsic structure of the group at hand.<>