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SUBGROUPS OF FINITE INDEX IN (2, 3, n)-TRIANGLE GROUPS

Published online by Cambridge University Press:  31 July 2012

W. WILSON STOTHERS
W. WILSON STOTHERS*
Affiliation:
Department of Mathematics, University Gardens, Glasgow, G12 8QW, Scotland
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Abstract

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For an integer n ≥ 7, let Δ(n) denote the (2, 3, n)-triangle group, and let M(n) be the positive integer determined by the conditions that Δ(n) has a subgroup of index m for all m ≥ M(n), but no subgroup of index M(n) − 1. The main purpose of the paper is to obtain information (bounds, in some cases explicit values) concerning the function M(n) (cf. Theorem 1). We also show that Δ(n) is replete (i.e., has a subgroup of index m for every integer m ≥ 1) if, and only if, n is divisible by 20 or by 30 (see Theorem 2).

Keywords

20D6020F67
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 3 , September 2012 , pp. 693 - 714
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

References

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