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    Tamburini, M.C. and Vsemirnov, M. 2006.


    Kondrat'ev, A. S. Makhnev, A. A. and Starostin, A. I. 1989. Finite groups. Journal of Soviet Mathematics, Vol. 44, Issue. 3, p. 237.


    Đoković, Dragomir Ž. 1988. Presentations of some finite simple groups. Journal of the Australian Mathematical Society, Vol. 45, Issue. 02, p. 143.


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  • Proceedings of the Edinburgh Mathematical Society, Volume 25, Issue 1
  • February 1982, pp. 65-68

Generators for the sporadic group Co3 as a (2, 3, 7) group

  • M. F. Worboys (a1)
  • DOI: http://dx.doi.org/10.1017/S0013091500004144
  • Published online: 01 January 2009
Abstract

A (2, 3, 7)-group is a group generated by two elements, one an involution and the other of order 3, whose product has order 7. Known finite simple examples of such groups are PSL(2, 7), PSL(2, p) where p is prime and p ≡ ±1 (mod 7), PSL(2, p3) where p is prime and p≢0, ±1 (mod 7), groups of Ree type of order q3(q3 + 1)(q − 1) where q = 32n+1 and n > 0, the sporadic group of order 23 · 3 · 5 · 7 · 11 · 19 discovered by Janko, and the Hall–Janko–Wales group of order 27 · 33 · 52 · 7 [4, 2]. G. Higman in an unpublished paper has shown that every sufficiently large alternating group is a (2, 3, 7)-group. Here we show that the sporadic group Co3 discovered by Conway [1] is a (2, 3, 7)-group.

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1.J. H. Conway , A Group of order 8, 315, 553, 613, 086, 720, 000, Bull. London Math. Soc. 1 (1969), 7988.

2.L. Finkelstein and A. Rudvalis , Maximal subgroups of the Hall–Janko–Wales group, J. Algebra 24 (1973), 486493.

3.D. G. Higman and C. C. Sims , A simple group of order 44, 352, 000, Math. Zeitschr. 105 (1968), 110113.

4.C. Sah , Groups related to compact Riemann surfaces, Acta Math. 123 (1969), 1342.

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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
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