Computing in permutation and matrix groups. II. Backtrack algorithm

Author:
Gregory Butler

Journal:
Math. Comp. **39** (1982), 671-680

MSC:
Primary 20-04; Secondary 20E25, 20G40

DOI:
https://doi.org/10.1090/S0025-5718-1982-0669659-5

MathSciNet review:
669659

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Abstract | References | Similar Articles | Additional Information

Abstract: 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.

**[1]**Gregory Butler,*Computational Approaches to Certain Problems in the Theory of Finite Groups*, Ph. D. Thesis, University of Sydney, 1979.**[2]**Gregory Butler,*Computing normalizers in permutation groups*, J. Algorithms**4**(1983), no. 2, 163–175. MR**699212**, https://doi.org/10.1016/0196-6774(83)90043-3**[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**, https://doi.org/10.1090/S0025-5718-1982-0669658-3

Gregory Butler,*Computing in permutation and matrix groups. II. Backtrack algorithm*, Math. Comp.**39**(1982), no. 160, 671–680. MR**669659**, https://doi.org/10.1090/S0025-5718-1982-0669659-5**[4]**Gregory Butler & John J. Cannon, "Computing in permutation and matrix groups. III: Sylow subgroups." (Manuscript.)**[5]**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****[6]**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.**[7]**Christoph M. Hoffman, "On the complexity of intersecting permutation groups and its relationship with graph isomorphism." (Manuscript.)**[8]**James F. Hurley and Arunas Rudvalis,*Finite simple groups*, Amer. Math. Monthly**84**(1977), no. 9, 693–714. MR**0466269**, https://doi.org/10.2307/2321249**[9]**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**, https://doi.org/10.1016/0097-3165(79)90018-9**[10]**Jeffrey S. Leon, personal communication.**[11]**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****[12]**Heinrich Robertz,*Eine Methode zur Berechnung der Automorphismengruppe einer endliche Gruppe*, Diplomarbeit, R. W. T. H. Aachen, 1976.**[13]**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) Amer. Math. Soc., Providence, R.I., 1971, pp. 191–195. SIAM-AMS Proc., Vol. IV. MR**0338135****[14]**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

DOI:
https://doi.org/10.1090/S0025-5718-1982-0669659-5

Keywords:
Backtrack algorithm,
permutation group,
matrix group

Article copyright:
© Copyright 1982
American Mathematical Society