A unital, that is, a block-design 2 - (q^3 + 1, q + 1,1), is embedded in a projective plane II of order q(2) if its points and blocks are points and lines of H. A unital embedded in PG(2, q(2)) is Hermitian if its points and blocks are the absolute points and non-absolute lines of a unitary polarity of PG(2, q(2)). A classical polar unital is a unital isomorphic, as a block-design, to a Hermitian unital. We prove that there exists only one embedding of the classical polar unital in PG(2, q(2)), namely the Hermitian unital. (C) 2017 Elsevier Inc. All rights reserved.

Embedding of classical polar unitals in PG(2, q(2))

Korchmaros, G;Siciliano, A;
2018

Abstract

A unital, that is, a block-design 2 - (q^3 + 1, q + 1,1), is embedded in a projective plane II of order q(2) if its points and blocks are points and lines of H. A unital embedded in PG(2, q(2)) is Hermitian if its points and blocks are the absolute points and non-absolute lines of a unitary polarity of PG(2, q(2)). A classical polar unital is a unital isomorphic, as a block-design, to a Hermitian unital. We prove that there exists only one embedding of the classical polar unital in PG(2, q(2)), namely the Hermitian unital. (C) 2017 Elsevier Inc. All rights reserved.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11563/156406
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