Commutative loops of exponent two and involutorial 3-nets with identity
type: Item
instance of: scholarly article
title: Commutative loops of exponent two and involutorial 3-nets with identity
zbMATH Open document ID: 0681.20043
DOI: 10.1007/BF00182398
author: Donato Saeli
author: Gabor Korchmáros
published in: Geometriae Dedicata
publication date: 1988-01-01T00:00:00Z
review text: 3-nets are one generalization of affine planes. To every quasigroup there corresponds a uniquely determined 3-net, and to every 3-net there corresponds a set of pairwise isostrophic quasigroups. In that sense, 3- nets are co-ordinatized by quasigroups. In this paper, the authors investigate 3-nets co-ordinatized by commutative loops of exponent two. The authors call them involutive 3-nets with identity. In particular, they consider direction-preserving collineation groups which stabilize the transversal line \(e_ t\) consisting of all points (x,x).
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 51A25
Mathematics Subject Classification ID: 51E15
zbMATH DE Number: 4114898
zbMATH Keywords: co-ordinatized by quasigroups
zbMATH Keywords: 3-nets
zbMATH Keywords: commutative loops of exponent two
zbMATH Keywords: collineation groups
Wikidata QID: Q59249300
reviewed by: Janez Ušan
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00182398
OpenAlex ID: W1966065124
description: scientific article; zbMATH DE number 4114898