Some finite translation planes arising from \(A_ 6\)-invariant ovoids of the Klein quadric
type: Item
instance of: scholarly article
title: Some finite translation planes arising from \(A_ 6\)-invariant ovoids of the Klein quadric
zbMATH Open document ID: 0705.51004
DOI: 10.1007/BF01230357
author: Mauro Biliotti
author: Gabor Korchmáros
published in: Journal of Geometry
publication date: 1990-01-01T00:00:00Z
review text: The authors enumerate (up to isomorphism) all translation planes of order \(p^ 2\), where p is a prime satisfying \(5\leq p\leq 19\), whose translation complement contains a subgroup \(\Gamma\) such that \(\Gamma\) modulo its scalars is isomorphic to \(A_ 6\). The basic technique used in the paper is the Klein correspondence, thereby reducing the problem to a study of \(A_ 6\)-invariant ovoids on the Klein quadric of PG(5,q). A computer was used for the cases \(q=17\) and \(q=19\).
Mathematics Subject Classification ID: 51A40
Mathematics Subject Classification ID: 51E20
zbMATH DE Number: 4157364
zbMATH Keywords: translation plane
zbMATH Keywords: ovoid
zbMATH Keywords: Klein quadric
Wikidata QID: Q59249293
reviewed by: Gary L. Ebert
MaRDI profile type: Publication
cites work: Q3851217
cites work: Q3694152
cites work: Orthogonal geometries over GF(2) and actions of extra-special 2-groups on translation planes
cites work: Some translation planes of order \(7^ 2\) which admit \(SL_ 2(9)\)
cites work: Some translation planes of order \(p^ 2\) and of extra-special type
cites work: The Klein correspondence and the ubiquity of certain translation planes
cites work: Collineation groups whose order is prime to the characteristic
cites work: Translation Planes of Dimension Two with Odd Characteristic
cites work: A characterization of some translation planes
full work available at URL: https://doi.org/10.1007/bf01230357
OpenAlex ID: W2045547026
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description: scientific article; zbMATH DE number 4157364