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.
|Number of pages||26|
|Journal||Journal of Algebra|
|Early online date||18 Sep 2014|
|Publication status||Published - 1 Jan 2015|