Algorithms for arithmetic groups with the congruence subgroup property

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.