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Algorithms for arithmetic groups with the congruence subgroup property

Authors
Journal
Journal of Algebra
0021-8693
Publisher
Elsevier
Identifiers
DOI: 10.1016/j.jalgebra.2014.08.027
Keywords
  • Algorithm
  • Arithmetic Group
  • Congruence Subgroup Property
  • Orbit-Stabilizer Problem
Disciplines
  • Computer Science
  • Mathematics

Abstract

Abstract 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.

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