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 and J. McKay,*The nonabelian simple groups 𝐺, \mid𝐺\mid<10⁶—maximal subgroups*, Math. Comp.**32**(1978), no. 144, 1293–1302. MR**0498831**, https://doi.org/10.1090/S0025-5718-1978-0498831-1**[3]**John McKay,*Computing with finite simple groups*, Proceedings of the Second International Conference on the Theory of Groups (Australian Nat. Univ., Canberra, 1973) Springer, Berlin, 1974, pp. 448–452. Lecture Notes in Math., Vol. 372. MR**0364431****[4]**John McKay,*Subgroups and permutation characters*, Computers in algebra and number theory (Proc. SIAM-AMS Sympos. Appl. Math., New York, 1970) Amer. Math. Soc., Providence, R.I., 1971, pp. 177–181. SIAM-AMS Proc., Vol. IV. MR**0372011****[5]**J. MCKAY, "The non-abelian simple groups*G*, . Character tables." (To appear.)**[6]**Robert Steinberg,*Generators for simple groups*, Canad. J. Math.**14**(1962), 277–283. MR**0143801**, https://doi.org/10.4153/CJM-1962-018-0**[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