We describe efficient algorithms for working with subgroups of . Operations discussed include join and meet, congruence testing, congruence closure, subgroup testing, cusp enumeration, supergroup lattice, generators and coset enumeration, and constructing a group from a list of generators. Introduction The set of linear fractional transformations of the form (1) known as Möbius transformations, has … Continue reading Manipulating Subgroups of the Modular Group