Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



The nonabelian simple groups $ G$, $ G<10\sp{6}$--minimal generating pairs

Authors: John McKay and Kiang Chuen Young
Journal: Math. Comp. 33 (1979), 812-814
MSC: Primary 20D05; Secondary 20F05
MathSciNet review: 521296
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Minimal (k, m, n) generating pairs and their associated presentations are defined for all nonabelian simple groups G, $ \vert G\vert < {10^6}$, excepting the family $ {\text{PSL}}(2,q)$. 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.

References [Enhancements On Off] (What's this?)

  • [1] J. J. CANNON, J. MCKAY & K. C. YOUNG, "The non-abelian simple groups G, $ \vert G\vert < {10^5}$. Presentations." (To appear.)
  • [2] J. FISCHER & J. MCKAY, "The non-abelian simple groups G, $ \vert G\vert < {10^6}$. 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, $ \vert G\vert < {10^6}$. 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.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 20D05, 20F05

Retrieve articles in all journals with MSC: 20D05, 20F05

Additional Information

Keywords: Finite simple groups, permutation groups, generating permutations
Article copyright: © Copyright 1979 American Mathematical Society

American Mathematical Society