Algorithms for arithmetic groups with the congruence subgroup property

Alla Detinko, Dane Flannery, Alexander Hulpke

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
Pages (from-to)234–259
Number of pages26
JournalJournal of Algebra
Volume421
Early online date18 Sep 2014
DOIs
Publication statusPublished - 1 Jan 2015
Externally publishedYes

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