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On some new classes of semifield planes
On some new classes of semifield planesopenaire +1 more source
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Ovals in commutative semifield planes
Archiv Der Mathematik, 1997A translation plane coordinatized by a semifield of odd order admits an orthogonal polarity whose absolute points form an oval \(\Omega\) (necessarily parabolic, having one point on the line at infinity). The collineation group of the plane which stabilizes such an \(\Omega\), acts 2-transitively on the affine points of \(\Omega\). In this paper, it is
Gabor Korchmáros, Korchmáros Gabor
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On central collineations of derived semifield planes
Journal of Geometry, 1978LetG denote the collineation group generated by the set of all affine central collineations in a derived semifield plane. We present a characterization of the Hall planes in terms of the order ofG. This essentially allows the extension of the theorems of Kirkpatrick and Rahilly on generalized Hall planes to arbitrary derived semifield planes.
Norman L Johnson, Johnson Norman
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Collineation groups of derived semifield planes
Archiv Der Mathematik, 1973N L Johnson, Johnson N L
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Transitive parabolic unitals in semifield planes
Journal of Geometry, 2006Every semifield plane with spread in PG(3,K), where K is a field admitting a quadratic extension K+, is shown to admit a transitive parabolic unital.
Norman L Johnson, Johnson Norman L
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On semifield planes of order 162
Siberian Mathematical Journal, 1996Using methods from \textit{H. Huang} and \textit{N. L. Johnson} [Discrete Math. 80, No. 1, 69-79 (1990; Zbl 0699.51003)], the authors determine all semifields planes of order \(16^2\) with \(GF(16)\) contained in the kernel such that the linear translation complement contains a subgroup of order \(2 \cdot 16^2\) (these planes admit a Baer involution ...
Podufalov, N. D. +3 more
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On the collineation groups of derived semifield planes
Mathematische Zeitschrift, 1983 Mauro Biliotti, Biliotti Mauro
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A note on the derived semifield planes of order 16
Aequationes Mathematicae, 1977 An affine plane ~" is tangentially transitive with respect to a subplane ~re if ~r admits a collineation group which fixes ~'e pointwise and acts transitive on each of the tangent pencils to ~r o. Jha [6] has studied finite translation planes ~" which are tangentially transitive with respect to ~re and has shown that if the order of ~is not 16 then ]rr[
N L Johnson, Johnson N L
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