On cyclic caps in projective spaces
type: Item
instance of: scholarly article
title: On cyclic caps in projective spaces
zbMATH Open document ID: 0860.51003
published in: Designs, Codes and Cryptography
publication date: 1996-11-18T00:00:00Z
review text: A cap in a projective space is a set of points no three of which are collinear. A cap is called complete if it is maximal subject to set-theoretical inclusion. Let \(G\) be a cyclic Singer group of the \(n\)-dimensional projective space \(PG( n,q)\). Let \(H\) be a subgroup of \(G\) and put \(|H|=N\). In this paper, the author studies the following problem: when is a point orbit of \(H\) a cap? A necessary and sufficient condition for this is derived and used to give a short proof of some results by \textit{E. Ebert} [Can. J. Math. 37, 1163-1175 (1985; Zbl 0577.51001)] and to show that small orbits are typically caps.
Mathematics Subject Classification ID: 51E21
Mathematics Subject Classification ID: 51E22
zbMATH DE Number: 934070
zbMATH Keywords: arcs
zbMATH Keywords: Singer group
zbMATH Keywords: caps
author: Tamás Szőnyi
reviewed by: Giorgio Faina
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 934070