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 Bol loop, Moufang loop, nilpotent, commutator, associator, minimally nonassociative

MSC Classifications:

20N05 show english descriptions Loops, quasigroups [See also 05Bxx] 20N05 - Loops, quasigroups [See also 05Bxx]

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