SL-unitals are unitals of order admitting a regular action of SL on the complement of some block. They can be obtained from affine SL-unitals via parallelisms. We compute a sharp upper bound for automorphism groups of affine SL-unitals and show that exactly two parallelisms are fixed by all automorphisms. In nonclassical SL-unitals obtained as closures of affine SL-unitals via those two parallelisms, we show that there is one block fixed under the full automorphism group.
Verena Möhler. "Automorphisms of (affine) SL-unitals." Innov. Incidence Geom. Algebr. Topol. Comb. 19 (1) 25 - 39, 2022. https://doi.org/10.2140/iig.2022.19.25