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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


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.)
  • James F. Hurley and Arunas Rudvalis, Finite simple groups, Amer. Math. Monthly 84 (1977), no. 9, 693–714. MR 466269, DOI 10.2307/2321249
  • Jeffrey S. Leon, An algorithm for computing the automorphism group of a Hadamard matrix, J. Combin. Theory Ser. A 27 (1979), no. 3, 289–306. MR 555799, DOI 10.1016/0097-3165(79)90018-9
  • 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.
  • Charles C. Sims, Determining the conjugacy classes of a permutation group, Computers in algebra and number theory (Proc. SIAM-AMS Sympos. Appl. Math., New York, 1970) SIAM-AMS Proc., Vol. IV, Amer. Math. Soc., Providence, R.I., 1971, pp. 191–195. MR 0338135
  • 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