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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Computing in permutation and matrix groups. II. Backtrack algorithm
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by Gregory Butler PDF
Math. Comp. 39 (1982), 671-680 Request permission


This is the second paper in a series which discusses computation in permutation and matrix groups of very large order. The essential aspects of a backtrack algorithm which searches these groups are presented. We then uniformly describe algorithms for computing centralizers, intersections, and set stabilizers, as well as an algorithm which determines whether two elements are conjugate.
    Gregory Butler, Computational Approaches to Certain Problems in the Theory of Finite Groups, Ph. D. Thesis, University of Sydney, 1979.
  • Gregory Butler, Computing normalizers in permutation groups, J. Algorithms 4 (1983), no. 2, 163–175. MR 699212, DOI 10.1016/0196-6774(83)90043-3
  • Gregory Butler and John J. Cannon, Computing in permutation and matrix groups. I. Normal closure, commutator subgroups, series, Math. Comp. 39 (1982), no. 160, 663–670. MR 669658, DOI 10.1090/S0025-5718-1982-0669658-3
  • Gregory Butler & John J. Cannon, "Computing in permutation and matrix groups. III: Sylow subgroups." (Manuscript.)
  • John J. Cannon, Software tools for group theory, The Santa Cruz Conference on Finite Groups (Univ. California, Santa Cruz, Calif., 1979) Proc. Sympos. Pure Math., vol. 37, Amer. Math. Soc., Providence, R.I., 1980, pp. 495–502. MR 604627
  • John J. Cannon, Robyn Gallagher & Kim McAllister, "STACKHANDLER: A language extension for low level set processing," Programming and Implementation Manual, TR 5, Computer-Aided Mathematics Project, Department of Pure Mathematics, University of Sydney, 1974. Christoph M. Hoffman, "On the complexity of intersecting permutation groups and its relationship with graph isomorphism." (Manuscript.)
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  • Jeffrey S. Leon, personal communication.
  • Brendan D. McKay, Computing automorphisms and canonical labellings of graphs, Combinatorial mathematics (Proc. Internat. Conf. Combinatorial Theory, Australian Nat. Univ., Canberra, 1977) Lecture Notes in Math., vol. 686, Springer, Berlin, 1978, pp. 223–232. MR 526749
  • Heinrich Robertz, Eine Methode zur Berechnung der Automorphismengruppe einer endliche Gruppe, Diplomarbeit, R. W. T. H. Aachen, 1976.
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  • Charles C. Sims, "Computation with permutation groups," Proc. Second Sympos. on Symbolic and Algebraic Manipulation (Los Angeles, 1971), S. R. Petrick (ed.), A. C. M., New York, 1971.
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Math. Comp. 39 (1982), 671-680
  • MSC: Primary 20-04; Secondary 20E25, 20G40
  • DOI:
  • MathSciNet review: 669659