On a general associativity law in groupoids
type: Item
instance of: scholarly article
title: On a general associativity law in groupoids
zbMATH Open document ID: 0768.20032
DOI: 10.1007/BF01299305
published in: Monatshefte für Mathematik
publication date: 1993-05-12T00:00:00Z
full work available at URL: https://eudml.org/doc/178552
review text: In the theory of nonassociative groupoids the main problem is to overcome the difficulties caused by the absence of the associativity law. In this paper we reduce calculations in a groupoid to calculations in a group. In order to do this certain transitivity properties of mappings on the groupoid are used. The main result is: if a general associativity law is satisfied in a division groupoid \(G\), then \(G\) is in fact a group.
Mathematics Subject Classification ID: 20N02
Mathematics Subject Classification ID: 20L05
Mathematics Subject Classification ID: 20N05
zbMATH DE Number: 164935
zbMATH Keywords: nonassociative groupoids
zbMATH Keywords: associativity law
zbMATH Keywords: division groupoid
author: Markku Niemenmaa
author: Tomáš Kepka
MaRDI profile type: Publication
cites work: Q5606623
cites work: Contributions to the Theory of Loops
cites work: On conjugacy classes in finite loops
cites work: On multiplication groups of loops
cites work: On representable pairs
OpenAlex ID: W1968053614
description: scientific article; zbMATH DE number 164935