Abstract:Let $\mathbb{P}$ be an algebraic number field. We provide a computational analog of the strong approximation theorem for finitely generated Zariski dense groups $H\leq \mathrm{SL}(n,\mathbb{P})$, $n$ prime. That is, we present algorithms to find the set of congruence quotients of $H$ modulo all maximal ideals of a finitely generated subring $R$ of $\mathbb{P}$ such that $H\leq \mathrm{SL}(n,R)$. The algorithms have been implemented in GAP. Potential applications are illustrated by a range of experiments in degree $2$, with a special focus on Bianchi groups.
| Subjects: | Group Theory (math.GR) |
| MSC classes: | 20-04, 20G15, 20H25, 22E40, 68W30 |
| Cite as: | arXiv:2605.23798 [math.GR] |
| (or arXiv:2605.23798v1 [math.GR] for this version) | |
| https://doi.org/10.48550/arXiv.2605.23798 arXiv-issued DOI via DataCite (pending registration) |
From: Dane Flannery [view email]
[v1]
Fri, 22 May 2026 15:57:58 UTC (23 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。