Geodesic
Fuchsian Subgroups of the Picard Group
Canadian journal of mathematics, Tome 28 (1976) no. 3, pp. 481-485

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The Picard group Γ = PSL2 (Z(i)) is the group of linear transformations with a, b, c, d Gaussian integers.Γ is of interest both as an abstract group and in automorphic function theory [10]. In [10] Waldinger constructed a subgroup H of finite index which is a generalized free product, while in [1] Fine showed that T is a semidirect product with the subgroup H, contained as a subgroup of finite index in the normal factor. 
Fine, Benjamin. Fuchsian Subgroups of the Picard Group. Canadian journal of mathematics, Tome 28 (1976) no. 3, pp. 481-485. doi: 10.4153/CJM-1976-049-3
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