Moufang loops with a unique nonidentity commutator (associator, square)
type: Item
instance of: scholarly article
title: Moufang loops with a unique nonidentity commutator (associator, square)
zbMATH Open document ID: 0695.20040
DOI: 10.1016/0021-8693(90)90087-5
author: Orin Chein
author: Edgar G. Goodaire
published in: Journal of Algebra
publication date: 1990-01-01T00:00:00Z
review text: A class of loops, called code loops, turns out to be Moufang loops which have some properties like a unique nonidentity associator, a unique nonidentity square, and a unique nonidentity commutator. Moufang loops with one or more of these properties play an important role for loops which have alternative loop rings. In this article, the authors study Moufang loops with the properties listed above. So, in Section 3, we have loops which have unique nonidentity commutators and/or associators, and some properties are investigated. In Section 4, the authors consider Moufang loops with a unique nonidentity square, and show that these are exactly the code loops studied by \textit{R. L. Griess} jun. [J. Algebra 100, 224-234 (1986; Zbl 0589.20051)].
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 17D05
zbMATH DE Number: 4138056
zbMATH Keywords: code loops
zbMATH Keywords: Moufang loops
zbMATH Keywords: alternative loop rings
zbMATH Keywords: commutators
zbMATH Keywords: associators
zbMATH Keywords: square
reviewed by: C. Pereira da Silva
MaRDI profile type: Publication
full work available at URL: 0021-8693(90)90087-5
OpenAlex ID: W2027508151
cites work: Q5515384
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description: scientific article; zbMATH DE number 4138056