Abstract

POMMERENKE, Christian  and  TORO, Margarita. Free subgroups of the parametrized modular group. Rev.colomb.mat. [online]. 2015, vol.49, n.2, pp.269-279. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v49n2.60445.

Abstract We study free subgroups of index four of the parametrized modular group Π, the subgroup of SL generated by and . There are eight free subgroups, four of which are normal and four are non-normal. Then we study the intersections of the normal subgroups. We give canonical presentations in terms of generators and relations. At the end of the paper we study connections between Π and the Bianchi groups, the two-parabolic group and a group from relativity theory.

Keywords : Parametrized modular group; free subgroups; Bianchi groups; Picard group; discrete relativity theory.

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