Transposition hypergroups: Noncommutative join spaces
type: Item
instance of: scholarly article
title: Transposition hypergroups: Noncommutative join spaces
zbMATH Open document ID: 0874.20051
author: James Jantosciak
published in: Journal of Algebra
publication date: 1997-11-06T00:00:00Z
full work available at URL: https://polipapers.upv.es/index.php/AGT/article/view/1963
review text: A transposition hyperqroup is a hypergroup \(H\) for which: \((b\setminus a)\cap(c/d)\neq\emptyset\) implies \(ad\cap bc\neq\emptyset\), for every \(a\), \(b\), \(c\), \(d\) in \(H\), where \(b\setminus a=\{x\in H\mid a\in bx\}\) and \(c/d=\{x\in H\mid c\in xd\}\). Introducing this notion, the author treats from a unique point of view several algebraic hyperstructures (join spaces, weak cogroups, double coset spaces, polygroups, canonical hypergroups, groups) instead to study them separately (as usually), all of them being transposition hypergroups. The (closed and reflexive) subhypergroups and the quotient spaces of a transposition hypergroup are studied. The three isomorphism theorems and the theorem of Jordan-Hölder of group theory are derived in the context of transposition hypergroups. The paper is very clear and very well written.
Mathematics Subject Classification ID: 20N20
zbMATH DE Number: 1014033
zbMATH Keywords: join spaces
zbMATH Keywords: weak cogroups
zbMATH Keywords: double coset spaces
zbMATH Keywords: polygroups
zbMATH Keywords: canonical hypergroups
zbMATH Keywords: transposition hypergroups
zbMATH Keywords: quotient spaces
zbMATH Keywords: isomorphism theorems
zbMATH Keywords: Jordan-Hölder theorem
reviewed by: Marin Guţan
MaRDI profile type: Publication
OpenAlex ID: W2016569951
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DOI: 10.1006/JABR.1997.6789
description: scientific article; zbMATH DE number 1014033