2022/03/31 by A. S. Detinko, Detinko, A. S., D. L. Flannery +3
Mathematics · #20-04 #20G15 #20H25 #68W30 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2203.17201
openalex publication_date 2022/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We initiate 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.