Article contents
On non-Hurwitz groups and non-congruence subgroups of the modular group
Published online by Cambridge University Press: 18 May 2009
Extract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
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
- Copyright
- Copyright © Glasgow Mathematical Journal Trust 1981
References
REFERENCES
1.Hartley, W. W., Ternary collineation groups, Ann. of Math. 27 (1925), 140–158.CrossRefGoogle Scholar
2.Leech, John, Generators for certain normal subgroups of (2, 3, 7), Proc. Cambridge Philos. Soc. 61 (1965), 321–332.CrossRefGoogle Scholar
3.Macbeath, A. M., Generators of the linear fractional groups, Proceedings of a Symposium of Pure Mathematics in Number Theory, Vol. XII, Houston (1967), 14–32.Google Scholar
4.Mitchell, H. H., Ternary linear groups, Trans. Amer. Math. Soc. 12 (1911), 207–242.CrossRefGoogle Scholar
5.Newman, Morris, Maximal normal subgroups of the modular group, Proc. Amer. Math. Soc. 19 (1968), 1138–44.CrossRefGoogle Scholar
You have
Access
- 22
- Cited by