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On an algorithm for finding a base and a strong generating set for a group given by generating permutations. (English) Zbl 0444.20001


MSC:

20-04 Software, source code, etc. for problems pertaining to group theory
20F05 Generators, relations, and presentations of groups
20B05 General theory for finite permutation groups
20B07 General theory for infinite permutation groups
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[1] John J. Cannon, Lucien A. Dimino, George Havas, and Jane M. Watson, Implementation and analysis of the Todd-Coxeter algorithm, Math. Comp. 27 (1973), 463 – 490. · Zbl 0314.20028
[2] John J. Cannon and George Havas, Defining relations for the Held-Higman-Thompson simple group, Bull. Austral. Math. Soc. 11 (1974), 43 – 46. · Zbl 0279.20027
[3] Marshall Hall Jr., The theory of groups, The Macmillan Co., New York, N.Y., 1959.
[4] John McKay and David Wales, The multipliers of the simple groups of order 604,800 and 50,232,960, J. Algebra 17 (1971), 262 – 272. · Zbl 0215.10202
[5] 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.
[6] CHARLES C. SIMS, ”Computation with permutation groups,” in Proc. Second Sympos. Symbolic and Algebraic Manipulation, Assoc. Comput. Mach., New York, 1971. · Zbl 0449.20002
[7] CHARLES C. SIMS, ”Some algorithms based on coset enumeration,” Unpublished notes, 1974.
[8] 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. · Zbl 0405.20001
[9] J. A. Todd, Abstract definitions for the Mathieu groups, Quart. J. Math. Oxford Ser. (2) 21 (1970), 421 – 424. · Zbl 0205.03901
[10] J. A. TODD & H. S. M. COXETER, ”A practical method for enumerating cosets of a finite abstract group,” Proc. Edinburgh Math. Soc., v. 5, 1936, pp. 26-34. · Zbl 0015.10103
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