Vol. 19, No. 1, 2021-2022

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Automorphisms of (affine) SL$(2,q)$-unitals

Verena Möhler

Vol. 19 (2021-2022), No. 1, 25–39
DOI: 10.2140/iig.2022.19.25
Abstract

SL((2,q)-unitals are unitals of order q admitting a regular action of SL((2,q) on the complement of some block. They can be obtained from affine SL((2,q)-unitals via parallelisms. We compute a sharp upper bound for automorphism groups of affine SL((2,q)-unitals and show that exactly two parallelisms are fixed by all automorphisms. In nonclassical SL((2,q)-unitals obtained as closures of affine SL((2,q)-unitals via those two parallelisms, we show that there is one block fixed under the full automorphism group.

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Keywords
design, unital, affine unital, automorphism, parallelism
Mathematical Subject Classification
Primary: 51A10
Secondary: 05E18
Milestones
Received: 19 March 2021
Revised: 14 September 2021
Accepted: 2 November 2021
Published: 7 April 2022
Authors
Verena Möhler
Karlsruhe
Germany