Results 61 to 70 of about 102 (87)

On semifield planes of order 162

Siberian Mathematical Journal, 1996
Using 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., Durakov, B. K., Kravtsova, O. V., Durakov, E. B.   +3 more
exaly   +3 more sources

Transitive parabolic unitals in semifield planes

Journal of Geometry, 2006
Every 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 Johnson
exaly   +2 more sources

On central collineations of derived semifield planes

Journal of Geometry, 1978
LetG 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 Johnson
exaly   +2 more sources

Autotopism groups of cyclic semifield planes [PDF]

Journal of Algebraic Combinatorics, 2011
Let \(V\) be an \(m\)-dimensional vector space over the finite field \(K\) with \(q^{n}\) elements, \(\sigma\) an automorphism of \(K\) and \(T\) an irreducible \(\sigma\)-linear operator on \(V\). Assume that the fixed field \(K_{0}\) of \(\sigma\) has \(q=p^{f}\) elements, \(p\) prime.
Ulrich Dempwolff
exaly   +3 more sources

Semifield planes with a transitive autotopism group

Archiv der Mathematik, 1994
Let \(\pi\) be a non-Desarguesian semifield plane of order \(p^ n\), where \(p\) is an odd prime number and \(n \geq 3\). Let \(G\) be the autotopism group of \(\pi\) relative to an autotopism triangle \(\Delta\). We prove that if the group \(\overline G\) induced by \(G\) on a side of \(\Delta\) is transitive on the non-vertex points of that side ...
Cordero, Minerva, Figueroa, Raúl F.
openaire   +2 more sources

Nuclear fusion in finite semifield planes

advg, 2004
Abstract We study the subplanes of finite semifield planes that are coordinatizable by subfields F of some semifield D such that F lies in at least two of the three seminuclear fields N ℓ(D), Nm (D), and Nr (D).
Jha, Vikram, Johnson, Norman L.
openaire   +1 more source

A note on commutative semifield planes

Advances in Geometry, 2017
Abstract Let q be an odd prime power. We prove that a planar function f from 𝔽 q to itself can be written as an affine Dembowski–Ostrom polynomial if and only if the projective plane derived from f is a commutative semifield plane.
openaire   +1 more source

A remark on symplectic semifield planes and Z 4-linear codes

Designs, Codes and Cryptography, 2012
Kantor and Williams (Trans Am Soc 356:895---938, 2004) introduced a family of non-desarguesian symplectic semifields of even order and studied a number of structures connected with such semifields; namely, symplectic spreads, orthogonal spreads and Z 4-linear codes. Also, they provided equivalence results concerning such objects, although under certain
LUNARDON, GUGLIELMO, G. Marino, O. Polverino, TROMBETTI, ROCCO   +3 more
openaire   +3 more sources

Finite semifields and projective planes

1963
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. This paper makes contributions to the structure theory of finite semifields, i.e., of finite nonassociative division algebras with unit.
openaire   +1 more source

Heisenberg groups, semifields, and translation planes

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Knarr, Norbert, Stroppel, Markus J.
openaire   +2 more sources