Three affine \(\mathrm{SL}(2,8)\)-unitals

DOI10.1007/S13366-022-00630-6zbMATH Open1525.51007arXiv2012.10134OpenAlexW4220750223MaRDI QIDQ6161422

Verena Möhler

Publication date: 27 June 2023

Published in: Beiträge zur Algebra und Geometrie (Search for Journal in Brave)

Abstract: $operatornameSL(2,q)$-unitals are unitals of order $q$ admitting a regular action of $operatornameSL(2,q)$ on the complement of some block. We introduce three non-classical affine $operatornameSL(2,8)$-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 $8$.

Full work available at URL: https://arxiv.org/abs/2012.10134

zbMATH Keywords

automorphismdesignunitalaffine unitalnon-classical unital

Mathematics Subject Classification ID

Other designs, configurations (05B30) Other finite linear geometries (51E26) Homomorphism, automorphism and dualities in linear incidence geometry (51A10)

Cites Work

• A non-classical unital of order four with many translations
• Automorphisms of unitary block designs
• Unitals admitting all translations
• Endliche Gruppen I

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