Some aspects of pregroups
type: Item
instance of: scholarly article
title: Some aspects of pregroups
zbMATH Open document ID: 0594.20073
DOI: 10.1007/BF01189861
published in: Archiv der Mathematik
publication date: 1986-01-01T00:00:00Z
review text: A pregroup is a set A, equipped with a ternary operation \(\lambda\) : \(A\times A\times A\to A\), satisfying axioms \[ I.\quad \lambda (p,q,p)=q;\quad \lambda (p,p,q)=q \] \[ II.\quad \lambda (r,\lambda (p,q,r),t)=\lambda (p,q,t)\quad \lambda (q,t,\lambda (p,q,r))=\lambda (p,t,r). \] In this paper the author develops the subject algebraically by defining the notion of normal subpregroups, quotient pregroups, free pregroups, etc. Finally the author discusses the concept of normality ''based at a point''.
Mathematics Subject Classification ID: 20N99
Mathematics Subject Classification ID: 20N10
Mathematics Subject Classification ID: 20A05
zbMATH DE Number: 3955259
zbMATH Keywords: ternary operation
zbMATH Keywords: axioms
zbMATH Keywords: normal subpregroups
zbMATH Keywords: quotient pregroups
zbMATH Keywords: free pregroups
author: S. A. Huq
MaRDI profile type: Publication
cites work: The ternary operation (𝑎𝑏𝑐)=𝑎𝑏⁻¹𝑐 of a group
cites work: Q3667051
cites work: Q3665899
full work available at URL: https://doi.org/10.1007/bf01189861
OpenAlex ID: W2041022911
description: scientific article; zbMATH DE number 3955259