Abelian by cyclic groups resulting in Moufang loops. (Q2882893)
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scientific article; zbMATH DE number 6032968
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Abelian by cyclic groups resulting in Moufang loops. |
scientific article; zbMATH DE number 6032968 |
Statements
11 May 2012
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finite loops
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Moufang loops
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groups
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normal Abelian subgroups
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Abelian by cyclic groups resulting in Moufang loops. (English)
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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.
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