Moufang's theorem

Statement

Suppose $L$ is a Moufang loop (?). Suppose $x,y,z$ are (not necessarily distinct) elements of $L$ such that $\! x * (y * z) = (x * y) * z$. Then, the subloop of $L$ generated by $x,y,z$ is a group.

Related facts

Appplications

• Moufang implies diassociative

Similar facts

• Artin's generalized theorem on alternative rings