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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. I. Normal closure, commutator subgroups, series
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by Gregory Butler and John J. Cannon PDF
Math. Comp. 39 (1982), 663-670 Request permission


This paper is the first in a series which discusses computation in permutation and matrix groups of very large order. The fundamental concepts are defined, and some algorithms which perform elementary operations are presented. Algorithms to compute normal closures, commutator subgroups, derived series, lower central series, and upper central series are presented.
    Gregory Butler, "The Schreier algorithm for matrix groups," SYMSAC’ 76 (Proc. 1976 A. C. M. Sympos. on Symbolic and Algebraic Computation, Yorktown Heights, N. Y., 1976), R. D. Jenks (ed.), A. C. M., New York, 1976, pp. 167-170. Gregory Butler, Computational Approaches to Certain Problems in the Theory of Finite Groups, Ph. D. Thesis, University of Sydney, 1979.
  • John J. Cannon, Computing local structure of large finite groups, 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. 161–176. MR 0367027
  • 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
  • George Havas, J. S. Richardson, and Leon S. Sterling, The last of the Fibonacci groups, Proc. Roy. Soc. Edinburgh Sect. A 83 (1979), no. 3-4, 199–203. MR 549854, DOI 10.1017/S0308210500011513
  • Jeffrey S. Leon, On an algorithm for finding a base and a strong generating set for a group given by generating permutations, Math. Comp. 35 (1980), no. 151, 941–974. MR 572868, DOI 10.1090/S0025-5718-1980-0572868-5
  • Charles C. Sims, Computational methods in the study of permutation groups, Computational Problems in Abstract Algebra (Proc. Conf., Oxford, 1967) Pergamon, Oxford, 1970, pp. 169–183. MR 0257203
  • 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, The existence and uniqueness of Lyons’ group, Finite groups ’72 (Proc. Gainesville Conf., Univ. Florida, Gainesville, Fla., 1972) North-Holland Math. Studies, Vol. 7, North-Holland, Amsterdam, 1973, pp. 138–141. MR 0354881
  • Charles C. Sims, "Some algorithms based on coset enumeration," 1974. (Manuscript.)
  • Charles C. Sims, Some group-theoretic algorithms, Topics in algebra (Proc. 18th Summer Res. Inst., Austral. Math. Soc., Austral. Nat. Univ., Canberra, 1978) Lecture Notes in Math., vol. 697, Springer, Berlin, 1978, pp. 108–124. MR 524367
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Math. Comp. 39 (1982), 663-670
  • MSC: Primary 20-04; Secondary 20F14, 20G40
  • DOI:
  • MathSciNet review: 669658