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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2410.04126 |
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| _version_ | 1866915866019364864 |
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| author | Abdukhalikov, Kanat Ball, Simeon Ho, Duy Popatia, Tabriz |
| author_facet | Abdukhalikov, Kanat Ball, Simeon Ho, Duy Popatia, Tabriz |
| contents | We consider the cyclic presentation of $PG(3,q)$ whose points are in the finite field $\mathbb{F}_{q^4}$ and describe the known ovoids therein. We revisit the set $\mathcal{O}$, consisting of $(q^2+1)$-th roots of unity in $\mathbb{F}_{q^4}$, and prove that it forms an elliptic quadric within the cyclic presentation of $PG(3,q)$. Additionally, following the work of Glauberman on Suzuki groups, we offer a new description of Suzuki-Tits ovoids in the cyclic presentation of $PG(3,q)$, characterizing them as the zeroes of a polynomial over $\mathbb{F}_{q^4}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04126 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ovoids in the cyclic presentation of PG(3,q) Abdukhalikov, Kanat Ball, Simeon Ho, Duy Popatia, Tabriz Combinatorics Number Theory We consider the cyclic presentation of $PG(3,q)$ whose points are in the finite field $\mathbb{F}_{q^4}$ and describe the known ovoids therein. We revisit the set $\mathcal{O}$, consisting of $(q^2+1)$-th roots of unity in $\mathbb{F}_{q^4}$, and prove that it forms an elliptic quadric within the cyclic presentation of $PG(3,q)$. Additionally, following the work of Glauberman on Suzuki groups, we offer a new description of Suzuki-Tits ovoids in the cyclic presentation of $PG(3,q)$, characterizing them as the zeroes of a polynomial over $\mathbb{F}_{q^4}$. |
| title | Ovoids in the cyclic presentation of PG(3,q) |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2410.04126 |