On the nilpotence class of commutative Moufang loops

Abstract

AbstractThe 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.