TY - GEN
T1 - Freeness and S-arithmeticity of rational Möbius groups
AU - Detinko, A. S.
AU - Flannery, D. L.
AU - Hulpke, A.
N1 - Publisher Copyright:
© 2023 American Mathematical Society.
PY - 2023
Y1 - 2023
N2 - 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[1b] of Z. We prove that a Möbius group G ≤ SL(2, R) is not free by showing that it has finite index in 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) containing G.
AB - 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[1b] of Z. We prove that a Möbius group G ≤ SL(2, R) is not free by showing that it has finite index in 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) containing G.
UR - https://www.scopus.com/pages/publications/85150838044
U2 - 10.1090/conm/783/15734
DO - 10.1090/conm/783/15734
M3 - Conference Publication
AN - SCOPUS:85150838044
SN - 9781470468040
T3 - Contemporary Mathematics
SP - 47
EP - 56
BT - Computational Aspects of Discrete Subgroups of Lie Groups
A2 - Detinko, Alla
A2 - Kapovich, Michael
A2 - Kontorovich, Alex
A2 - Sarnak, Peter
A2 - Schwartz, Richard
PB - American Mathematical Society
T2 - Virtual Conference on Computational Aspects of Discrete Subgroups of Lie Groups, 2021
Y2 - 14 June 2021 through 18 June 2021
ER -