Algorithms for arithmetic groups with the congruence subgroup property

Alla Detinko; Dane Flannery; Alexander Hulpke

doi:10.1016/j.jalgebra.2014.08.027

Algorithms for arithmetic groups with the congruence subgroup property

Alla Detinko, Dane Flannery, Alexander Hulpke

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

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 language	English
Pages (from-to)	234–259
Number of pages	26
Journal	Journal of Algebra
Volume	421
Early online date	18 Sep 2014
DOIs	https://doi.org/10.1016/j.jalgebra.2014.08.027
Publication status	Published - 1 Jan 2015
Externally published	Yes

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KW - Arithmetic group

KW - Congruence subgroup property

KW - Orbit-stabilizer problem

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JO - Journal of Algebra

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Algorithms for arithmetic groups with the congruence subgroup property

Abstract

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