Translation extensions of the classical modular group
Troels Jørgensen, Antonio Lascurain, Thea Pignataro · Complex Variables Theory and Application An International Journal · 1992
The class of Kleinian groups which are extreme with respect to Jorgensen's inequality encompasses continuous families of geometrically finite groups as well as uncountably many geometrically infinite groups, Such groups may be obtained as extensions of the classical modular group.An infinite number of non-isomorphic extreme discrete groups arise this way; some, like the Picard group, are of co-finite volume.Other examples are obtained by extending certain triangle groups.