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On the nilpotence class of commutative Moufang loops

Published online by Cambridge University Press:  24 October 2008

J. D. H. Smith
J. D. H. Smith
Affiliation:
Technische Hochschule, Darmstadt, West Germany
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Abstract

The nilpotence class of the free commutative Moufang loop on n generators (n > 3) is the maximum allowed by the Bruck-Slaby Theorem, namely n − 1. This is proved by setting up a presentation of an extension of the loop's multiplication group as a nilpotent group of class at most 2n − 2, and then using the Macdonald-Wamsley technique of nilpotent group theory to show that this class is exactly 2n − 2.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 84 , Issue 3 , November 1978 , pp. 387 - 404
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

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