Abstract
With a subgroup of finite index in the (2,3,7) triangle group, we associate a quintuple of non-negative integers (u,p,e,f,g), with u ≥1 and u=84(p−1)+21e+28f+36g. We show that, with three exceptions, each quintuple satisfying the conditions corresponds to a subgroup. The proof uses coset diagrams.
The result can be viewed as a result on the classical modular group. With this interpretation, the main theorem is related to two recent papers on the latter group.
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Stothers, W.W. Subgroups of the (2,3,7) triangle group. Manuscripta Math 20, 323–334 (1977). https://doi.org/10.1007/BF01171125
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DOI: https://doi.org/10.1007/BF01171125