Abelian by cyclic groups resulting in Moufang loops.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1246.20063
DOI: 10.1515/JGT.2010.089
author: Stephen M. III Gagola
published in: Journal of Group Theory
publication date: 2012-05-11T00:00:00Z
Mathematics Subject Classification ID: 20N05
zbMATH DE Number: 6032968
zbMATH Keywords: finite loops
zbMATH Keywords: Moufang loops
zbMATH Keywords: groups
zbMATH Keywords: normal Abelian subgroups
MaRDI profile type: Publication
title: Abelian by cyclic groups resulting in Moufang loops.
review text: It was shown by \textit{O. Chein} and \textit{A. Rajah} [in Commentat. Math. Univ. Carol. 41, No. 2, 237-244 (2000; Zbl 1038.20045)] that if \(m\) is odd then every Moufang loop \(G\) of order \(2m\) which contains a normal Abelian subgroup \(N\) of order \(m\) is a group. However, if \(G\) is a Moufang loop with a normal Abelian subgroup \(N\) of odd order where \(G/N\) is cyclic of order divisible by three then there is no guarantee that \(G\) is a group. The purpose of the author in this paper is to determine when a Moufang loop is a group under certain conditions.
reviewed by: C. Pereira da Silva
description: scientific article; zbMATH DE number 6032968