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September 2012 Translation planes of odd order via Dembowski--Ostrom polynomials
Ulrich Dempwolff, Peter Müller
Osaka J. Math. 49(3): 771-794 (September 2012).

Abstract

We describe a class of translation planes whose orders are of the form $q^{n}$, where $n$ is odd and $q$ is an odd prime power $>3$. These planes have the property that a translation complement fixes a triangle and acts transitively on the set of non-vertices of each side. The planes form an odd order analogue to the planes of Kantor--Williams [17] which have even order. The construction of the planes is based on a certain type of Dembowski--Ostrom polynomials.

Citation

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Ulrich Dempwolff. Peter Müller. "Translation planes of odd order via Dembowski--Ostrom polynomials." Osaka J. Math. 49 (3) 771 - 794, September 2012.

Information

Published: September 2012
First available in Project Euclid: 15 October 2012

zbMATH: 1261.51005
MathSciNet: MR2993066

Subjects:
Primary: 51E15
Secondary: 50E20

Rights: Copyright © 2012 Osaka University and Osaka City University, Departments of Mathematics

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Vol.49 • No. 3 • September 2012
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