Hecke Groups
The modular group can be generalized to the Hecke groups, named for Erich Hecke, and defined as follows.
The Hecke group Hq is the discrete group generated by
- and where
The modular group Γ is isomorphic to H3 and they share properties and applications – for example, just as one has the free product of cyclic groups
- more generally one has
which corresponds to the triangle group (2,q,∞). There is similarly a notion of principal congruence subgroups associated to principal ideals in For small values of q, one has:
Read more about this topic: Modular Group
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