I read about how Hecke groups are a particular generalisation of the modular group, generalising one of the generators of the modular group to $z\mapsto z + \lambda$. Have people studied generalisations of the other generator of the modular group, perhaps generalising to $z \mapsto \dfrac{-1}{z^n}$ ?
generalisations of the modular group
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group-theory
modular-group
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0It would be $z \mapsto \sqrt[n]{\dfrac{-1}{z}}$, but the roots in the upper-half plane would all have to be identified. – 2011-02-25