On the Bruck-Slaby theorem for commutative Moufang loops (Q1972529)
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scientific article; zbMATH DE number 1429635
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Bruck-Slaby theorem for commutative Moufang loops |
scientific article; zbMATH DE number 1429635 |
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On the Bruck-Slaby theorem for commutative Moufang loops (English)
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2 August 2000
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The classical Bruck-Slaby theorem (a commutative Moufang loop (CML) with \(n\) (\(n\geq 2\)) generators is centrally nilpotent of class at most \(n-1\)) was proved in its weakened version (any finite CML of period 3 is centrally nilpotent) by Yu. I. Manin (1972) and by J. D. H. Smith (1985). Now, the author gives a simple proof of the theorem: A finitely generated commutative Moufang loop is centrally nilpotent.
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alternative algebras
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central nilpotence classes
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finitely generated commutative Moufang loops
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