Algorithms for arithmetic groups with the congruence subgroup property

作者：Detinko A S; Flannery D L^*; Hulpke A

来源：Journal of Algebra, 2015, 421: 234-259.

DOI：10.1016/j.jalgebra.2014.08.027

• Algorithm
• Arithmetic group
• Congruence subgroup property
• Orbit-stabilizer problem

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, Z(m)) is vital to this work. All algorithms have been implemented in GAP.

• 出版日期2015-1-1