Zariski density and computing with S-integral groups

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

doi:10.1016/j.jalgebra.2023.02.024

Zariski density and computing with S-integral groups

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

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

Abstract

We generalize our methodology for computing with Zariski dense subgroups of SL(n,Z) and Sp(n,Z), to accommodate input dense subgroups H of SL(n,Q) and Sp(n,Q). A key task, backgrounded by the Strong Approximation theorem, is computing a minimal congruence overgroup of H. Once we have this overgroup, we may describe all congruence quotients of H. The case n=2 receives particular attention.

Original language	English
Pages (from-to)	93-105
Number of pages	13
Journal	Journal of Algebra
Volume	624
Early online date	30 Mar 2023
DOIs	https://doi.org/10.1016/j.jalgebra.2023.02.024
Publication status	Published - 15 Jun 2023

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10.1016/j.jalgebra.2023.02.024Licence: CC BY

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title = "Zariski density and computing with S-integral groups",

abstract = "We generalize our methodology for computing with Zariski dense subgroups of SL(n,Z) and Sp(n,Z), to accommodate input dense subgroups H of SL(n,Q) and Sp(n,Q). A key task, backgrounded by the Strong Approximation theorem, is computing a minimal congruence overgroup of H. Once we have this overgroup, we may describe all congruence quotients of H. The case n=2 receives particular attention.",

keywords = "Algorithm, Linear group, S-arithmetic, S-integral, Strong approximation, Zariski density",

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

note = "Funding Information: We thank Centre International de Rencontres Math{\'e}matiques, The Institute for Computational and Experimental Research in Mathematics, and Mathematisches Forschungsinstitut Oberwolfach, for support received through the Research in Pairs, Collaborate@ICERM, and Research Fellowship programmes. We thank Willem de Graaf for his assistance. The third author's work has been supported in part by NSF Grant DMS-1720146 and Simons Foundation Grant 852063 , which are both gratefully acknowledged. Publisher Copyright: {\textcopyright} 2023 The Author(s)",

year = "2023",

month = jun,

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doi = "10.1016/j.jalgebra.2023.02.024",

language = "English",

volume = "624",

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journal = "Journal of Algebra",

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T1 - Zariski density and computing with S-integral groups

AU - Detinko, A. S.

AU - Flannery, D. L.

AU - Hulpke, A.

N1 - Funding Information: We thank Centre International de Rencontres Mathématiques, The Institute for Computational and Experimental Research in Mathematics, and Mathematisches Forschungsinstitut Oberwolfach, for support received through the Research in Pairs, Collaborate@ICERM, and Research Fellowship programmes. We thank Willem de Graaf for his assistance. The third author's work has been supported in part by NSF Grant DMS-1720146 and Simons Foundation Grant 852063 , which are both gratefully acknowledged. Publisher Copyright: © 2023 The Author(s)

PY - 2023/6/15

Y1 - 2023/6/15

N2 - We generalize our methodology for computing with Zariski dense subgroups of SL(n,Z) and Sp(n,Z), to accommodate input dense subgroups H of SL(n,Q) and Sp(n,Q). A key task, backgrounded by the Strong Approximation theorem, is computing a minimal congruence overgroup of H. Once we have this overgroup, we may describe all congruence quotients of H. The case n=2 receives particular attention.

AB - We generalize our methodology for computing with Zariski dense subgroups of SL(n,Z) and Sp(n,Z), to accommodate input dense subgroups H of SL(n,Q) and Sp(n,Q). A key task, backgrounded by the Strong Approximation theorem, is computing a minimal congruence overgroup of H. Once we have this overgroup, we may describe all congruence quotients of H. The case n=2 receives particular attention.

KW - Algorithm

KW - Linear group

KW - S-arithmetic

KW - S-integral

KW - Strong approximation

KW - Zariski density

UR - https://www.scopus.com/pages/publications/85150858828

U2 - 10.1016/j.jalgebra.2023.02.024

DO - 10.1016/j.jalgebra.2023.02.024

M3 - Article

AN - SCOPUS:85150858828

SN - 0021-8693

VL - 624

SP - 93

EP - 105

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Zariski density and computing with S-integral groups

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