Results 261 to 270 of about 29,113 (284)

Pencils of translation ovals in translation planes

Geometriae Dedicata, 1994
Let \({\mathcal T}\) be a translation plane of even order \(q\) with translation line \(I_ \infty\). An oval \({\mathcal O}\) in \({\mathcal T}\) is called a translation oval if \(I_ \infty\) is a tangent at a point \(a\) and if the stabilizer of \({\mathcal O}\) in the translation group acts transitively on \({\mathcal O}\setminus\{a\}\).
Glynn, D. G., Steinke, G. F.
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SOME CHARACTERIZATIONS OF DESARGUESIAN TRANSLATION PLANES

Journal of Algebra and Its Applications, 2006
In this note we consider finite translation planes with large translation complements. In particular, we characterize finite affine Desarguesian translation planes in two ways, according to the existence of subgroups in the translation complement that are divisible by relatively large integers, together with modest additional restrictions.
Brozovic, Douglas P., Ho, Chat Yin
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A characterization of «likeable» translation planes

Rendiconti del Circolo Matematico di Palermo, 1983
A translation plane of order \(q^ 2\) is said to be 'likeable' when it has kern \(GF(q)\) and when its linear translation complement contains a group of order \(q^ 2\) whose elation subgroup consists of elements, which, when the plane is constructed from a spread in \(PG(3,q)\), fix a regulus. Such planes are studied in this paper, mostly in terms of \(
Fink, J. B., Johnson, N. L., Wilke, F. W.   +2 more
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Smooth projective translation planes

Geometriae Dedicata, 1995
A projective or affine plane is called smooth if point and line space are endowed with smooth structures such that the geometric operations of joining and intersecting are smooth. The author of the paper under review has produced examples of smooth projective planes and of smooth affine translation planes.
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Nest replaceable translation planes

Journal of Geometry, 1989
A longstanding problem in the field of finite translation planes is the determination of a meaningful classification. Although this is far from being solved in general, substantial progress has occurred for finite translation planes of dimension 2. The article under review is in this vein. Further, it also gives a characterization of planes constructed
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Quasigroups and translation planes

Journal of Geometry, 1992
A quasigroup \((Q,\cdot)\) is said to be medial if \((x\cdot y)\cdot(z\cdot t)=(x\cdot z)\cdot(y\cdot t)\) for all \(x,y,z,t\in Q\), and is called idempotent if \(x\cdot x=x\) for all \(x\in Q\). If \((R,+,\cdot)\) is the coordinatizating ring of a translation plane and the kernel of \(R\) contains at least one element \(k\) distinct from 0 and 1, then
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On Translations in General Plane Geometries

American Journal of Mathematics, 1938
In a well-known paper, Hilbelt 1 has characterized the Euclidean and hyperbolic plane geometries by mere group and continuity axioms. He gets all the motions at once by requiring the existence of sufficiently many rotations. The present paper tries to point out how the existence of more and more translations gradually specializes the rather general ...
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Translation Planes

2008
Susan Barwick, Gary Ebert
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Symplectic translation planes

2003
This monograph is about symplectic translation planes, with particular regard to those of even order. A characteristic property is the existence of completely regular line-ovals, which relies on some properties of classical groups, especially the symplectic and orthogonal ones.
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Translation Planes

1995
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