A class of non-ordinary half-planes
type: Item
instance of: scholarly article
title: A class of non-ordinary half-planes
zbMATH Open document ID: 0697.51003
DOI: 10.1007/BF03322631
author: Carla Fiori
published in: Results in Mathematics
publication date: 1990-01-01T00:00:00Z
review text: A set G of permutations on E is called 2-homogeneous if it acts regular on the 2-subsets of E; G is termed planar by the author if it can be partitioned into subsets M of G which act regular on points and \(\forall \alpha \in M\) \(\forall \beta \in G\setminus M\) \(\exists x\in E:\) \(\alpha (x)=\beta (x)\). Non-planarity is shown for some G contained in the group of affine transformations of certain non-planar nearfields or quasifields. Such G yield examples of non-ordinary half planes, thus answering a question from \textit{D. G. Glynn} [Ars Comb. 19A, 309-342 (1985; Zbl 0561.51013)].
Mathematics Subject Classification ID: 51A99
Mathematics Subject Classification ID: 51E30
Mathematics Subject Classification ID: 12K05
Mathematics Subject Classification ID: 16Y30
zbMATH DE Number: 4142909
zbMATH Keywords: half-plane
zbMATH Keywords: non-planar nearfield
zbMATH Keywords: non-planar quasifield
reviewed by: Horst Szambien
MaRDI profile type: Publication
cites work: Incidence Systems associated with Non-Planar Nearfields
cites work: Q5186260
cites work: Q3659962
cites work: Projective and non-projective near-fields
description: scientific article; zbMATH DE number 4142909