Algorithms for arithmetic groups with the congruence subgroup property

A. S. Detinko; D. L. Flannery; A. Hulpke

doi:10.1016/j.jalgebra.2014.08.027

Algorithms for arithmetic groups with the congruence subgroup property

A. S. Detinko, D. L. Flannery, A. Hulpke

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › 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
DOIs	https://doi.org/10.1016/j.jalgebra.2014.08.027
Publication status	Published - 1 Jan 2015

Keywords

Algorithm
Arithmetic group
Congruence subgroup property
Orbit-stabilizer problem

Access to Document

10.1016/j.jalgebra.2014.08.027

Cite this

@article{d256c906bf0e4e5392bc1451af8baab2,

title = "Algorithms for arithmetic groups with the congruence subgroup property",

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.",

keywords = "Algorithm, Arithmetic group, Congruence subgroup property, Orbit-stabilizer problem",

author = "Detinko, \{A. S.\} and Flannery, \{D. L.\} and A. Hulpke",

note = "Publisher Copyright: {\textcopyright} 2014 Elsevier Inc.",

year = "2015",

month = jan,

day = "1",

doi = "10.1016/j.jalgebra.2014.08.027",

language = "English",

volume = "421",

pages = "234--259",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Algorithms for arithmetic groups with the congruence subgroup property

AU - Detinko, A. S.

AU - Flannery, D. L.

AU - Hulpke, A.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - 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.

AB - 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.

KW - Algorithm

KW - Arithmetic group

KW - Congruence subgroup property

KW - Orbit-stabilizer problem

UR - https://www.scopus.com/pages/publications/84908592546

U2 - 10.1016/j.jalgebra.2014.08.027

DO - 10.1016/j.jalgebra.2014.08.027

M3 - Article

SN - 0021-8693

VL - 421

SP - 234

EP - 259

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Algorithms for arithmetic groups with the congruence subgroup property

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this