On planar functions
type: Item
instance of: scholarly article
title: On planar functions
zbMATH Open document ID: 0702.20016
DOI: 10.1016/0021-8693(90)90071-U
author: Yutaka Hiramine
published in: Journal of Algebra
publication date: 1990-01-01T00:00:00Z
review text: Planar functions serve to describe planes of order n admitting a certain type of collineation group of order \(n^ 2\) [cf. \textit{P. Dembowski} and \textit{T. G. Ostrom}; Math. Z. 103, 239-258 (1968; Zbl 0163.424)]. All known examples occur (for odd n) in elementary abelian p-groups and belong to semifield planes. The author gives a general description of such planar functions. He also studies the general case and obtains some non-existence results; e.g., he rules out all orders n of the form \(n=pq\), where p and q are primes for which p divides \(q^ m+1\) for some positive integer m.
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 51E15
Mathematics Subject Classification ID: 05B25
zbMATH DE Number: 4150485
zbMATH Keywords: affine plane
zbMATH Keywords: collineation group
zbMATH Keywords: elementary abelian p-groups
zbMATH Keywords: semifield planes
zbMATH Keywords: planar functions
reviewed by: Dieter Jungnickel
MaRDI profile type: Publication
cites work: Q5521595
cites work: Planes of order \(n\) with collineation groups of order \(n^ 2\)
cites work: Q5545191
cites work: Q5577154
cites work: Automorphisms of p-groups of semifield type
cites work: Q5683869
description: scientific article; zbMATH DE number 4150485