Algorithms for arithmetic groups with the congruence subgroup property

Detinko, A. S.; Flannery, D. L.; Hulpke, A.

Abstract

© 2014 Elsevier Inc. We develop practical techniques to compute with arithmetic groups H≤SL(n,Q) for n>. 2. Our approach relies on constructing a principal congruence subgroup in H. Problems solved include testing membership in H, analyzing the subnormal structure of H, and the orbit-stabilizer problem for H. Effective computation with subgroups of GL(n,Zm) is vital to this work. All algorithms have been implemented in GAP.

Citation

Detinko, A. S., Flannery, D. L., & Hulpke, A. (2015). Algorithms for arithmetic groups with the congruence subgroup property. Journal of Algebra, 421, 234-259. https://doi.org/10.1016/j.jalgebra.2014.08.027

• Journal Article Type: Article
• Online Publication Date: Sep 18, 2014
• Publication Date: Jan 1, 2015
• Deposit Date: May 16, 2019
• Journal: Journal of Algebra
• Print ISSN: 0021-8693
• Electronic ISSN: 1090-266X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 421
• Pages: 234-259
• DOI: https://doi.org/10.1016/j.jalgebra.2014.08.027
• Keywords: Algorithm; Arithmetic group; Congruence subgroup property; Orbit-stabilizer problem
• Public URL: https://hull-repository.worktribe.com/output/1794521
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0021869314004736?via%3Dihub