Results 61 to 70 of about 102 (85)
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A note on the Boerner-lantz semifield planes
Journal of Geometry, 1992Für die von \textit{V. Boerner-Lantz} [J. Geom. 27, 112-118 (1986; Zbl 0604.12020)] angegebene Konstruktion endlicher distributiver Quasikörper (= semifield) wird die Anzahl der Isomorphietypen so erhaltbarer projektiver Ebenen vorgegebener Ordnung \(p^ 4\) bestimmt: Für \(p\equiv 1\bmod 4\) ist diese Anzahl \(1/4(p-1)\), für \(p\equiv 3\bmod 4\) ist ...
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The centre of a finite semifield plane is a geometric invariant
Archiv Der Mathematik, 1988It is well known that the left, middle, and right nucleus, of a finite semifield are geometric invariants, that is, they do not change if the plane is recoordinatized by another semifield. On the other hand, the nucleus of the semified is in general not a geometric invariant.
N L Johnson, Johnson N L
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Derived semifield planes with affine elations
Journal of Geometry, 1982Derived semifield planes admitting non trivial affine elations with more than one centre are examined in detail and several new examples of such plantes are constructed. A new characterization of the Hall planes of even order among derived semifield planes is also given.
Mauro Biliotti, Biliotti Mauro
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Nuclear fusion in finite semifield planes
advg, 2004Abstract 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.
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Semifield planes with a transitive autotopism group
Archiv Der Mathematik, 1994Let \(\pi\) 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.
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A note on commutative semifield planes
Advances in Geometry, 2017Abstract 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.
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A remark on symplectic semifield planes and Z 4-linear codes
Designs, Codes and Cryptography, 2012Kantor 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 +3 more
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Finite semifields and projective planes
1963NOTE: 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.
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Heisenberg groups, semifields, and translation planes
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Knarr, Norbert, Stroppel, Markus J.
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Net replacements in the Hughes-Kleinfeld semifield planes
Journal of Geometry, 2010If \(\alpha\) is an automorphism of a field \(K\), the cone \(C_\alpha\) in \(PG(3,k)\) consists of the points \(\{ (x_0,x_1,x_2,x_3) \) \( \;| \;x_0^\alpha x_1 = x_2^{\alpha + 1}\}\) with vertex \(v_0 = (0,0,0,1).\) A set of planes of \(PG(3,k)\) which partitions these points without \(v_0\) is a flock of \(C_\alpha\).
Cherowitzo, William E. +1 more
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