Elsevier

Journal of Algebra

Volume 421, 1 January 2015, Pages 234-259
Journal of Algebra

Algorithms for arithmetic groups with the congruence subgroup property

https://doi.org/10.1016/j.jalgebra.2014.08.027Get rights and content
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Abstract

We develop practical techniques to compute with arithmetic groups HSL(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.

Keywords

Algorithm
Arithmetic group
Congruence subgroup property
Orbit-stabilizer problem

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