Three Affine SL(2,8)-Unitals

Abstract

$\mathrm{SL}(2,q)$-unitals are unitals of order $q$ admitting a regular action of $\mathrm{SL}(2,q)$ on the complement of some block. We introduce three non-classical affine $\mathrm{SL}(2,8)$-unitals and their full automorphism groups. Each of those three affine unitals can be completed to at least two non-isomorphic unitals, leading to six pairwise non-isomorphic unitals of order $8$.

10 pages; references updated. arXiv admin note: text overlap with arXiv:2012.10116, arXiv:2012.10129

References in corpus (3)

• Automorphisms of (Affine) SL(2,q)-Unitals
• Moufang sets generated by translations in unitals
• Parallelisms and Translations of (Affine) SL(2,q)-Unitals

Cited by in corpus (1)

• Automorphisms of (Affine) SL(2,q)-Unitals