تقرير
Dihedralizing the quaternions
| العنوان: | Dihedralizing the quaternions |
|---|---|
| المؤلفون: | Macauley, Matthew |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Group Theory, Mathematics - History and Overview, 20D99, 05C25 |
| الوصف: | In this paper, we take the classic dihedral and quaternion groups and explore questions like "what if we replace $i=e^{2\pi i/4}$ in $Q_8$ with a larger root of unity?" and "what if we add a reflection to $Q_8$?" The delightful answers reveal lesser-known families like the dicyclic, diquaternion, semidihedral, and semiabelian groups, which come to life with visuals such as Cayley graphs, cycle graphs, and subgroup lattices. Comment: Expository and recreational. Full color version of a forthcoming Monthly article. 14 pages, 17 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2310.13087 |
| رقم الأكسشن: | edsarx.2310.13087 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |