Free subgroups of the parametrized modular group

We study free subgroups of index four of the parametrized modular group Π, the subgroup of SL(2; Z[ξ]) generated by (10 ξ1) and (01 -10). 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 prese...

Full description

Autores:
Pommerenke, Christian
Toro, Margarita
Tipo de recurso:
Article of journal
Fecha de publicación:
2015
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/66461
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/66461
http://bdigital.unal.edu.co/67489/
Palabra clave:
51 Matemáticas / Mathematics
Parametrized modular group
free subgroups
Bianchi groups
Picard group
discrete relativity theory
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
Description
Summary:We study free subgroups of index four of the parametrized modular group Π, the subgroup of SL(2; Z[ξ]) generated by (10 ξ1) and (01 -10). 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 and the Bianchi groups, the two-parabolic group and a group from relativity theory.