Leon, Jeffrey S. On an algorithm for finding a base and a strong generating set for a group given by generating permutations. (English) Zbl 0444.20001 Math. Comput. 35, 941-974 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 7 ReviewsCited in 24 Documents 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 Keywords:Schreier-Todd-Coxeter-Sims method; strong generating set; ordered base; orbits of a permutation group; coset representatives; presentations Citations:Zbl 0275.20018; Zbl 0401.20009; Zbl 0215.10002; Zbl 0253.20001; Zbl 0405.20001; Zbl 0314.20028 PDFBibTeX XMLCite \textit{J. S. Leon}, Math. Comput. 35, 941--974 (1980; Zbl 0444.20001) Full Text: DOI References: [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 · Zbl 0449.20002 [7] CHARLES C. SIMS, ”Some algorithms based on coset enumeration,” Unpublished notes, 1974.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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.