An oval partition of the central units of certain semifield planes
type: Item
instance of: scholarly article
title: An oval partition of the central units of certain semifield planes
zbMATH Open document ID: 0865.51002
DOI: 10.1016/0012-365X(94)00376-T
author: Yanyan Li
published in: Discrete Mathematics
publication date: 1996-10-07T00:00:00Z
review text: Let the translation plane \(\pi\) be coordinatised by the commutative semified \((D,+, \circ)\) of even order \(q^N\) and assume that the middle nucleus of \(D\) is isomorphic to \(GF(q)\). An affine point \(I\) of \(\pi\) not on the coordinate axes is called a central unit if the semifield obtained from \(D\) by recoordinatising \(\pi\) with \(I\) as unit point is also commutative. The authors show that all nonzero points on the translation oval \(\{(x,x\circ x)\mid x\in D\}\) are central units and that all other central units are obtained by applying middle nucleus homologies to this translation oval. It follows that the set of central units is partitioned into \(q-1\) translation ovals minus the origin.
reviewed by: Norbert Knarr
Mathematics Subject Classification ID: 51A40
Mathematics Subject Classification ID: 12K10
zbMATH DE Number: 932532
zbMATH Keywords: central unit
zbMATH Keywords: commutative semified
zbMATH Keywords: translation oval
MaRDI profile type: Publication
cites work: Q3983240
cites work: Polarities in translation planes
cites work: Q5683869
cites work: Q3817217
cites work: Q4028439
cites work: Q4276291
cites work: A Class of Projective Planes
cites work: Finite translation planes
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description: scientific article; zbMATH DE number 932532