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# Bol Loops of Nilpotence Class Two

Published:2007-04-01
Printed: Apr 2007
• Orin Chein
• Edgar G. Goodaire
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## Abstract

Call a non-Moufang Bol loop \emph{minimally non-Moufang} if every proper subloop is Moufang and \emph{minimally nonassociative} if every proper subloop is associative. We prove that these concepts are the same for Bol loops which are nilpotent of class two and in which certain associators square to $1$. In the process, we derive many commutator and associator identities which hold in such loops.
 Keywords: Bol loop, Moufang loop, nilpotent, commutator, associator, minimally nonassociative