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