Arcs in \(\mathrm{PG}(n,q)\) fixed by \(A_5\) and \(A_6\)
type: Item
instance of: scholarly article
title: Arcs in \(\mathrm{PG}(n,q)\) fixed by \(A_5\) and \(A_6\)
zbMATH Open document ID: 0848.51007
DOI: 10.1007/BF01223038
author: Christine M. O'Keefe
author: Leo Storme
published in: Journal of Geometry
publication date: 1996-10-28T00:00:00Z
review text: A \(k\)-arc in a projective space is a set of \(k\) points, no three of which are collinear. The author determines the \(k\) arcs in \(\mathrm{PG}(n,q)\) which are fixed by primitive groups isomorphic to \(A_5\) or \(A_6\). The best known examples are \(q+1\) arcs: in general these are normal rational curves and are conics in \(\mathrm{PG}(2,q)\) and twisted cubics in \(\mathrm{PG}(3,q)\). The other cases turn out to be 6-arcs or 10-arcs.
Mathematics Subject Classification ID: 51E21
Mathematics Subject Classification ID: 20B25
zbMATH DE Number: 872720
zbMATH Keywords: k-arcs
zbMATH Keywords: projective space
reviewed by: Theodore G. Ostrom
describes a project that uses: AXIOM
MaRDI profile type: Publication
cites work: Q3684278
cites work: The non-classical 10-arc of PG(4,9)
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cites work: \(k\)-arcs and dual \(k\)-arcs
cites work: Primitive arcs in \(\mathrm{PG}(2,q)\)
cites work: Q5640331
full work available at URL: https://doi.org/10.1007/bf01223038
OpenAlex ID: W3013710320
description: scientific article; zbMATH DE number 872720