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Search: MSC category 20N05 ( Loops, quasigroups [See also 05Bxx] )

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1. CJM 2007 (vol 59 pp. 296)

Chein, Orin; Goodaire, Edgar G.
Bol Loops of Nilpotence Class Two
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
Category:20N05

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