Abstract
Every finite subunital of any generalized hermitian unital is itself a hermitian unital; the embedding is given by an embedding of quadratic field extensions. In particular, a generalized hermitian unital with a finite subunital is a hermitian one (i.e., it originates from a separable field extension).
Highlights
If C|R is inseparable, H(C|R) is the projection of an ordinary quadric Q in some projective space of dimension at least 3 from a subspace of codimension 1 in the nucleus of Q, see [4, 2.2]
By an O’Nan configuration, we mean four blocks intersecting in six points of the unital (i.e., a (62 43) configuration)
Naming this configuration in honor of O’Nan [8] is customary in the context of unitals, see [2, p. 87]; the configuration is named after Veblen and Young in the axiomatics of projective spaces, or after Pasch in the context of ordered (Euclidean) geometry
Summary
For Assertion (TRA), we apply the translation with center p that maps the intersection of the block joining p and z with B to the point z. Uniqueness of B is a consequence of (NON), and the rest of Assertion (TRA) follows from the fact that B is the image of B under a translation with center p. The intersection of the lines containing the blocks B and B in the projective plane PG(2, C) is a point fixed by that elation, and contained in the tangent line at p.
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