تقرير
The Lattice of Group Topologies on a Group
| العنوان: | The Lattice of Group Topologies on a Group |
|---|---|
| المؤلفون: | Peng, Dekui |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - General Topology, Mathematics - Group Theory, 54A10, 20F18 |
| الوصف: | For an infinite group $G$, the set of group topologies, $\mathcal{L}_G$, forms a complete lattice. It is known that $\mathcal{L}_G$ is modular if $G$ is abelian but the same result does not hold for nilpotent groups. We prove that the lattice $\mathcal{L}_G$ is semi-modular if and only if $\mathcal{L}_{G/Z}$ is semi-modular, where $Z$ is the centre. As a corollary, for every nilpotent group $G$, the lattice $\mathcal{L}_G$ is semi-modular. Moreover, in the famous Kourovka Notebook, several questions about $\mathcal{L}_G$ were formalized by Arnautov. We answer two of them in this note. Comment: 11 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2310.08269 |
| رقم الأكسشن: | edsarx.2310.08269 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |