@article{f71c93d5061c4172a11389db9a21a70d,
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,
day = "15",
doi = "10.1016/j.jalgebra.2023.02.024",
language = "English",
volume = "624",
pages = "93--105",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press Inc.",
}