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On non-Hurwitz groups and non-congruence subgroups of the modular group

Published online by Cambridge University Press:  18 May 2009

Jeffrey Cohen
Jeffrey Cohen
Affiliation:
University of Pittsburgh, Pittsburgh, Pennsylvania 15260
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In this note homomorphisms of (2, 3, n) = 〈x, y: x2 = y3 = (xy)n = 1) into PSL3(q) are considered. Of particular interest is (2, 3, 7) whose finite factors are referred to as Hurwitz groups. It is known (see [3]) that for certain q, PSL2(q) is a Hurwitz group, so that one might suppose that PSL3(q) is a natural place to search for new Hurwitz groups. This intuition turns out to be ill-founded, for as we shall see all Hurwitz subgroups of PSL3(q) have already been discovered in [3].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 22 , Issue 1 , January 1981 , pp. 1 - 7
Copyright
Copyright © Glasgow Mathematical Journal Trust 1981

References

REFERENCES

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