Permutation group algorithms based on partitions, I: Theory and algorithms

Authors:
Jeffrey S. Leon
Affiliations:
Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, Illinois 60680, U.S.A.
Venue:
Journal of Symbolic Computation - Special issue on computational group theory: part 2
Year:
1991

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Abstract

A technique for computing in permutation groups of high degree is developed. The technique uses the idea of successive refinement of ordered partitions, introduced by B. McKay in connection with the graph isomorphism problem, to supplement the techniques of base and strong generating set developed earlier by Sims. Applications to a number of specific problems in computational group theory are presented.