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

Published online by Cambridge University Press:  20 January 2009

M. F. Worboys
M. F. Worboys
Affiliation:
School of Mathematics and ComputingLeeds PolytechnicCalverley StreetLeeds LS1 3HE.
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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 G. Higman in an unpublished paper has shown that every sufficiently large alternating group is a (2, 3, 7)-group.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.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 25 , Issue 1 , February 1982 , pp. 65 - 68
Copyright
Copyright © Edinburgh Mathematical Society 1982

References

REFERENCES

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