On some flag-transitive non-classical \(c.C_ 2\)-geometries
type: Item
instance of: scholarly article
title: On some flag-transitive non-classical \(c.C_ 2\)-geometries
zbMATH Open document ID: 0769.51003
published in: European Journal of Combinatorics
publication date: 1993-05-16T00:00:00Z
review text: A \(c.C_ 2\)-geometry is a residually connected geometry which is an extension of a generalized quadrangle by a circle geometry (the intersection property is not assumed). The author constructs five flag- transitive geometries of this type, which appear to be new. These geometries have point sets of sizes 160, 80, 896, 448, 448 (with two pairs of quotients involved). The quadrangle residues of these geometries are isomorphic to the unique quadrangle of order (3,5) or to its dual [cf. \textit{S. E. Payne}, Proc. Boca Raton, 1990, Congr. Numerantium 77, 5- 29 (1990)]. The new geometries are constructed as coset geometries from groups described by generators and relations [cf. the author, Eur. J. Comb. 12, No. 2, 159-181 (1991; Zbl 0735.51011)]. The geometry on 896 points is also constructed from the unitary vector space \(GF(4)^ 8\).
reviewed by: Theo Grundhöfer
Mathematics Subject Classification ID: 51E12
Mathematics Subject Classification ID: 51E24
zbMATH DE Number: 167698
zbMATH Keywords: extended generalized quadrangle
zbMATH Keywords: flag-transitive geometries
author: Satoshi Yoshiara
MaRDI profile type: Publication
full work available at URL: eujc.1993.1010
OpenAlex ID: W2006764345
DOI: 10.1006/EUJC.1993.1010
description: scientific article; zbMATH DE number 167698