## Osaka Journal of Mathematics

### Translation planes of odd order via Dembowski--Ostrom polynomials

#### 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.

#### Article information

Source
Osaka J. Math., Volume 49, Number 3 (2012), 771-794.

Dates
First available in Project Euclid: 15 October 2012

https://projecteuclid.org/euclid.ojm/1350306596

Mathematical Reviews number (MathSciNet)
MR2993066

Zentralblatt MATH identifier
1261.51005

Subjects
Primary: 51E15: Affine and projective planes
Secondary: 50E20

#### Citation

Dempwolff, Ulrich; Müller, Peter. Translation planes of odd order via Dembowski--Ostrom polynomials. Osaka J. Math. 49 (2012), no. 3, 771--794. https://projecteuclid.org/euclid.ojm/1350306596

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