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arXiv · 2008.11445

Moufang sets generated by translations in unitals

Theo Grundhöfer·Markus J. Stroppel·Hendrik Van Maldeghem
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Abstract

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.

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Theo Grundhöfer, Markus J. Stroppel, Hendrik Van Maldeghem. 2020-08-26. Moufang sets generated by translations in unitals. https://doi.org/10.1002/jcd.21813

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