Non-crystallographic tail-triangle C-groups of rank 4 and interlacing number 2
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866912112011378688 |
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| author | Loyola, Mark L. Leyrita, Nonie Elvin S. Penas, Ma. Louise Antonette N. De Las |
| author_facet | Loyola, Mark L. Leyrita, Nonie Elvin S. Penas, Ma. Louise Antonette N. De Las |
| contents | This work applies the modular reduction technique to the Coxeter group of rank 4 having a star diagram with labels 5, 3, and $k = 3, 4, 5, \text{ or } 6$. As moduli, we use the primes in the quadratic integer ring $\mathbb{Z}[τ]$, where $τ= \frac{1 + \sqrt{5}}{2}$, the golden ratio. We prove that each reduced group is a C-group, regardless of the prime used in the reduction. We also classify each reduced group as a reflection group over a finite field, whenever applicable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_02598 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Non-crystallographic tail-triangle C-groups of rank 4 and interlacing number 2 Loyola, Mark L. Leyrita, Nonie Elvin S. Penas, Ma. Louise Antonette N. De Las Group Theory 20F55, 51F15, 51F25, 52B11, 52B15 This work applies the modular reduction technique to the Coxeter group of rank 4 having a star diagram with labels 5, 3, and $k = 3, 4, 5, \text{ or } 6$. As moduli, we use the primes in the quadratic integer ring $\mathbb{Z}[τ]$, where $τ= \frac{1 + \sqrt{5}}{2}$, the golden ratio. We prove that each reduced group is a C-group, regardless of the prime used in the reduction. We also classify each reduced group as a reflection group over a finite field, whenever applicable. |
| title | Non-crystallographic tail-triangle C-groups of rank 4 and interlacing number 2 |
| topic | Group Theory 20F55, 51F15, 51F25, 52B11, 52B15 |
| url | https://arxiv.org/abs/2202.02598 |