Congruence subgroups of the minimal covolume arithmetic Kleinian group

Autor:	Amir Džambić
Rok vydání:	2010
Předmět:	Normal subgroup Orientation (vector space) Fuchsian group Mathematics::Group Theory Quaternion algebra Group (mathematics) Kleinian group General Mathematics Quaternion group Arithmetic Relatively hyperbolic group Mathematics
Zdroj:	Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg. 80:265-273
ISSN:	1865-8784 0025-5858
DOI:	10.1007/s12188-010-0037-9
Popis:	We consider the problem of finding the normal subgroups of the orientation preserving subgroup Δ+ of the [3,5,3]-Coxeter group with the factor group isomorphic to $\operatorname{\mathrm{PSL}}_{2}(\mathbb {F}_{q})$ . We identify all such groups with particular congruence subgroups of an arithmetic subgroup of PSL 2(ℂ) derived from a quaternion algebra over a quartic field. The result can be interpreted as a generalization of the Macbeath’s result on the classification of finite linear groups as Hurwitz groups to 3-dimensional hyperbolic space.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::5cc2ead7940ecbea124264742636f5bb https://doi.org/10.1007/s12188-010-0037-9 Zobrazit plný text záznamu Full text from SpringerLink