Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Detinko, AllaFlannery, DaneHulpke, Alexander2024-10-172024-10-172022https://oa.tib.eu/renate/handle/123456789/16974https://doi.org/10.34657/15996We explore a new computational approach to a classical problem: certifying non-freeness of (2-generator, parabolic) Möbius subgroups of SL(2, Q). The main tools used are algorithms for Zariski dense groups and algorithms to compute a presentation of SL(2, R) for a localization R = Z[1/b] of Z. We prove that a Möbius subgroup G is not free by showing that it has finite index in the relevant SL(2, R). Further information about the structure of G is obtained; for example, we compute the minimal subgroup of finite index in SL(2, R) that contains G.engFree groupMöbius groupArithmetic groupAlgorithmSoftware510Report