تقرير
Discrete two-generator subgroups of ${\rm PSL_2}$ over non-archimedean local fields
| العنوان: | Discrete two-generator subgroups of ${\rm PSL_2}$ over non-archimedean local fields |
|---|---|
| المؤلفون: | Conder, Matthew J., Schillewaert, Jeroen |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Group Theory, Mathematics - Geometric Topology, 20E08, 22E40 |
| الوصف: | Let $K$ be a non-archimedean local field with residue field of characteristic $p$. We give necessary and sufficient conditions for a two-generator subgroup $G$ of ${\rm PSL_2}(K)$ to be discrete, where either $K=\mathbb{Q}_p$ or $G$ contains no elements of order $p$. We give a practical algorithm to decide whether such a subgroup $G$ is discrete. We also give practical algorithms to decide whether a two-generator subgroup of either ${\rm SL_2}(\mathbb{R})$ or ${\rm SL_2}(K)$ (where $K$ is a finite extension of $\mathbb{Q}_p$) is dense. A crucial ingredient for this work is a structure theorem for two-generator groups acting by isometries on a $\Lambda$-tree. Comment: 19 pages, 5 figures, 1 table. Version 2 has some minor updates |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2208.12404 |
| رقم الأكسشن: | edsarx.2208.12404 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |