New flag-transitive affine planes of even order
type: Item
instance of: scholarly article
title: New flag-transitive affine planes of even order
zbMATH Open document ID: 0852.51005
author: Michael E. Williams
author: William M. Kantor
published in: Journal of Combinatorial Theory. Series A
publication date: 1996-07-09T00:00:00Z
review text: Let \(V\) be a vector space of dimension \(2k\) over \(GF(q)\) with a nonsingular quadratic form \(Q\). An orthogonal spread is a family of \(q^{k - 1} + 1\) totally singular \(k\)-spaces such that each non-zero singular vector is in exactly one member of the family. The bilinear form \(Q(u + v) - Q(u) - Q(v)\) defines a symplectic structure. For \(q^m > 8,q\) even, let \(m, m_1, \dots\) be a sequence of distinct divisors of \(m\) such that \(m_i\) is divisible by \(m_{i + 1}\). The authors use a process of flipping back forth between symplectic and orthogonal spreads and together with various subfields of \(GF(q^m)\) to construct flag transitive affine planes.
Mathematics Subject Classification ID: 51E15
Mathematics Subject Classification ID: 51A40
Mathematics Subject Classification ID: 20B25
zbMATH DE Number: 883797
zbMATH Keywords: flag transitive affine planes
reviewed by: Theodore G. Ostrom
MaRDI profile type: Publication
OpenAlex ID: W2153049080
DOI: 10.1006/JCTA.1996.0033
description: scientific article; zbMATH DE number 883797