Translation planes of order 25 admitting a quaternion group of homologies with affine axis
type: Item
instance of: scholarly article
title: Translation planes of order 25 admitting a quaternion group of homologies with affine axis
zbMATH Open document ID: 0756.51006
DOI: 10.1007/BF03323090
author: Günter Heimbeck
published in: Results in Mathematics
publication date: 1992-09-27T00:00:00Z
review text: \textit{G. Mason} and \textit{T. G. Ostrom} [Geom. Dedicata 17, 307-322 (1985; Zbl 0566.51020)] have shown that the irregular nearfield plane of order 25 and the plane \(E(5)\) of extra-special type are two translation planes of order 25 that admit a quaternion group of homologies with an affine axis. In the paper under review the author shows that these are the only translation planes of order 25 with this property.
Mathematics Subject Classification ID: 51A40
zbMATH DE Number: 62173
zbMATH Keywords: quaternion group
zbMATH Keywords: homologies with affine axis
zbMATH Keywords: translation planes of order 25
reviewed by: Gary L. Ebert
MaRDI profile type: Publication
cites work: Q3891315
cites work: Some translation planes of order \(p^ 2\) and of extra-special type
cites work: Elementary abelian 2-groups on the line at infinity of translation planes
cites work: Q3704520
cites work: A new class of finite translation planes obtained from the exceptional near-fields
cites work: A characterization of some translation planes
full work available at URL: https://doi.org/10.1007/bf03323090
OpenAlex ID: W2078284905
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description: scientific article; zbMATH DE number 62173