Groups, triality, and hyperquasigroups.
type: Item
instance of: scholarly article
title: Groups, triality, and hyperquasigroups.
zbMATH Open document ID: 1252.20066
author: J. D. H. Smith
published in: Journal of Pure and Applied Algebra
publication date: 2012-06-08T00:00:00Z
review text: This paper is concerned with the algebraic structures known as hyperquasigroups, which are introduced as refinements of quasigroups. Hyperquasigroups were introduced to provide a more symmetrical approach to quasigroups, and a far-reaching implementation of triality. The aim of this paper is to establish comparable connections between hyperquasigroups and groups. The author introduces the key concept of the Cayley graph of a hyperquasigroup. According to the author within the Cayley graph provides a striking geometrical characterization of hyperquasigroups. The author focuses in the last two sections of the paper on the role of triality in hyperquasigroups, taking advantage of an orthant structure within the reflexion-inversion space to recover classical quasigroup information from a hyperquasigroup.
reviewed by: C. Pereira da Silva
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 20N20
Mathematics Subject Classification ID: 08A68
zbMATH DE Number: 6043586
zbMATH Keywords: quasigroups
zbMATH Keywords: triality
zbMATH Keywords: hyperquasigroups
zbMATH Keywords: groups
zbMATH Keywords: Latin squares
MaRDI profile type: Publication
full work available at URL: j.jpaa.2011.08.014
OpenAlex ID: W1996440833
Wikidata QID: Q122155276
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DOI: 10.1016/J.JPAA.2011.08.014
description: scientific article; zbMATH DE number 6043586