Moufang sets generated by translations in unitals

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 $\mathrm{SL}(2,{\mathbb{F}}_q)$ (as in all classical unitals and also in some non-classical examples), or $\mathrm{PSL}(2,{\mathbb{F}}_q)$, or a Suzuki or a Ree group. Moreover, $G$ is semi-regular outside the special block.

Cited by in corpus (3)

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