A characterization of Buekenhout-Metz unitals in PG\((2,q^ 2)\), \(q\) even
A unital (Hermitian arc) \(U\) in \(PG(2,q^2)\) is a set of \(q^3 + 1\) points such that the intersections of lines with \(U\) either consists of a single point or \(q + 1\) points. The absolute points and non-absolute lines of a non-degenerate unitary polarity form a ``classical unital''. The authors use the term ``\(B\)-unital'' to denote any unital constructed from an ovoid in \(PG(3,q)\) by a method of Buekenhout. If the ovoid is an elliptic quadric, they call it a \(B\)-\(M\) unital. [Note: In another paper reviewed in this same edition of Zbl, the authors use the term ``\(B\)-\(M\) unital'' with the same meaning as ``\(B\)-unital'' in the present paper.] The main result of the present paper is that if \(q\) is a power of 2, a \(B\)-unital \(U\) in \(PG(2,q^2)\) is a \(B\)-\(M\) unital if there is a point \(A\) on \(U\) such that the stabilizer of \(A\) in the linear collineation group fixing \(U\) has a subgroup which is sharply transitive on \(U\)-\(A\).
scientific article; zbMATH DE number 843608