Results 221 to 230 of about 86,943 (261)

SOME CLASSES OF TRANSLATION PLANES

The Quarterly Journal of Mathematics, 1984
This article considers the following. Let \(\pi\) be a finite translation plane of order \(p^ r\) with an autotopism group G which has an orbit of length \(p^ r\)-p on \(\ell_{\infty}\), the line at infinity. The authors make the following additional assumptions: (a) p is an odd prime and \(r=2\); (b) G acts faithfully on \(\ell_{\infty}\).
Cohen, Stephen D., Ganley, Michael J.
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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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The translation planes of order 49

Designs, Codes and Cryptography, 1995
The authors determine the quantity of classes of isomorphic translation planes of order 49. They report on the computer search for spreads in \(PG (3,7)\) and on classifying the spreads with the computer program NAUTY that looks for graph isomorphisms. The search results in a list of 1347 translation planes in which known planes formerly given by other
Rudolf Mathon, Gordon F. Royle
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A family of translation planes

Australas. J Comb., 2010
Summary: An infinite family of non-Desarguesian translation planes of order \(q^4\) with kernel \(\text{GF}(q^2)\) is constructed, for any odd prime power \(q\). The collineation group of each plane has orbits of lengths 1, \(q^2\), and \(q^4- q^2\) on the translation line.
Andrew Hudson, Tim Penttila
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Doubly β-Derived Translation Planes

Designs, Codes and Cryptography, 2003
Let \(q>3\) be an odd prime power. A chain of circles in the Miquelian inversive plane \(M(q)\) is a collection of \({1\over 2}(q+3)\) circles such that every point covered by some circle in this set lies on exactly two circles from the collection. Using the correspondence between points and circles of \(M(q)\) and lines and reguli of a regular spread \
Abatangelo, V., Larato, Bambina
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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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A Classification of Semi-Translation Planes

Canadian Journal of Mathematics, 1969
The classification of certain types of projective planes has recently been of considerable interest to both geometers and group theorists. Due in part to the current general interest in finite mathematics and the developments connecting group theory and finite geometry, the Lenz-Barlotti classification of finite projective planes (2; 10), in particular,
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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 of order 27

Designs, Codes and Cryptography, 1994
Up to isomorphism there are exactly seven, already known translation planes of order 27. The author shows this with the help of a computer and describes the seven types by invariants that play an important role in the computer search. Independently of the computer proof it is shown which of these types occur in the case that there is an elation in the ...
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Homologies in Translation Planes

Proceedings of the London Mathematical Society, 1973
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