Minimally nonassociative nilpotent Moufang loops.
type: Item
instance of: scholarly article
title: Minimally nonassociative nilpotent Moufang loops.
zbMATH Open document ID: 1033.20077
DOI: 10.1016/S0021-8693(03)00343-0
author: Orin Chein
author: Edgar G. Goodaire
published in: Journal of Algebra
publication date: 2003-10-22T00:00:00Z
review text: The authors consider the following question: Which varieties of Moufang loops have the property that the minimally nonassociative loops in the variety are precisely those which are indecomposable and which can be generated by three elements? The paper investigates the variety of centrally nilpotent Moufang loops and finds that while this variety as a whole does not have the property in question, the subvariety consisting of Moufang loops which are centrally nilpotent of class 2 does.
Mathematics Subject Classification ID: 20N05
zbMATH DE Number: 1995433
zbMATH Keywords: commutative Moufang loops
zbMATH Keywords: Abelian groups
zbMATH Keywords: associators
zbMATH Keywords: 3-generator loops
zbMATH Keywords: varieties of Moufang loops
zbMATH Keywords: minimally nonassociative loops
zbMATH Keywords: indecomposable loops
zbMATH Keywords: centrally nilpotent loops
reviewed by: C. Pereira da Silva
MaRDI profile type: Publication
cites work: Q5515384
cites work: Minimally nonassociative commutative Moufang loops
cites work: Q3024358
cites work: Loops whose loop rings are alternative
cites work: Moufang loops with a unique nonidentity commutator (associator, square)
cites work: Moufang Loops of Small Order. I
cites work: Moufang loops of small order
cites work: An "Extra" Law for Characterizing Moufang Loops
cites work: Q4332927
cites work: On loops of odd order. II
cites work: Q4950146
cites work: Q3322274
cites work: Nilpotence of finite Moufang 2-loops
cites work: Q3253828
cites work: Moufang loops of class 2 and cubic forms
cites work: Q4762449
cites work: A Class of Simple Moufang Loops
cites work: Q3998783
cites work: Generators of nonassociative simple Moufang loops over finite prime fields
description: scientific article; zbMATH DE number 1995433