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