The nonabelian simple groups , --minimal generating pairs

Authors:
John McKay and Kiang Chuen Young

Journal:
Math. Comp. **33** (1979), 812-814

MSC:
Primary 20D05; Secondary 20F05

DOI:
https://doi.org/10.1090/S0025-5718-1979-0521296-9

MathSciNet review:
521296

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Abstract: Minimal (*k, m, n*) generating pairs and their associated presentations are defined for all nonabelian simple groups *G*, , excepting the family . A complete set of minimal (2, *m, n*) generating permutations of minimal degree is tabulated for these *G*. The set is complete in the sense that any minimal generating pair for *G* will satisfy the same presentation as exactly one of the listed pairs.

**[1]**J. J. CANNON, J. MCKAY & K. C. YOUNG, "The non-abelian simple groups*G*, . Presentations." (To appear.)**[2]**J. FISCHER & J. MCKAY, "The non-abelian simple groups*G*, . Maximal subgroups,"*Math. Comp.*, v. 32, 1978, pp. 1293-1302. MR**0498831 (58:16867)****[3]**J. MCKAY, "Computing with finite simple groups,"*Proc. Second Internat. Conf. Theory of Groups*, Lecture Notes in Math., vol. 372, Springer-Verlag, Berlin, New York, 1974, pp. 448-452. MR**0364431 (51:685)****[4]**J. MCKAY, "Subgroups and permutation characters,"*Computers in Algebra and Number Theory*, SIAM-AMS Proceedings, vol. 4, 1970, Amer. Math. Soc., Providence, R. I., 1971, pp. 177-181. MR**0372011 (51:8228)****[5]**J. MCKAY, "The non-abelian simple groups*G*, . Character tables." (To appear.)**[6]**R. STEINBERG, "Generators for simple groups,"*Canad. J. Math.*, v. 14, 1962, pp. 277-283. MR**0143801 (26:1351)****[7]**K. C. YOUNG,*Computing with Finite Groups*, Ph. D. thesis, McGill University, Montreal, Canada, 1975.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1979-0521296-9

Keywords:
Finite simple groups,
permutation groups,
generating permutations

Article copyright:
© Copyright 1979
American Mathematical Society