Moufang sets generated by translations in unitals
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866915059303710720 |
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| author | Grundhöfer, Theo Stroppel, Markus J. Van Maldeghem, Hendrik |
| author_facet | Grundhöfer, Theo Stroppel, Markus J. Van Maldeghem, Hendrik |
| contents | We consider unitals of order $q$ with two points which are centers of translation groups of order $q$. The group $G$ generated by these translations induces a Moufang set on the block joining the two points. We show that $G$ is either $\operatorname{SL}(2,\mathbb{F}_q)$ (as in all classical unitals and also in some non-classical examples), or $\operatorname{PSL}(2,\mathbb{F}_q)$, or a Suzuki or a Ree group. Moreover, $G$ is semi-regular outside the special block. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_11445 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Moufang sets generated by translations in unitals Grundhöfer, Theo Stroppel, Markus J. Van Maldeghem, Hendrik Group Theory Combinatorics 05E20 (Primary) 05B30, 51A10 (Secondary) We consider unitals of order $q$ with two points which are centers of translation groups of order $q$. The group $G$ generated by these translations induces a Moufang set on the block joining the two points. We show that $G$ is either $\operatorname{SL}(2,\mathbb{F}_q)$ (as in all classical unitals and also in some non-classical examples), or $\operatorname{PSL}(2,\mathbb{F}_q)$, or a Suzuki or a Ree group. Moreover, $G$ is semi-regular outside the special block. |
| title | Moufang sets generated by translations in unitals |
| topic | Group Theory Combinatorics 05E20 (Primary) 05B30, 51A10 (Secondary) |
| url | https://arxiv.org/abs/2008.11445 |