On Two Problems Related to Associators of Moufang Loops

A Moufang loop $M$ of order $3^{19}$ is constructed, together with a pair $a$, $b$ of elements of $M$, such that the set of all elements of $M$ associating with $a$ and $b$ is not a subloop. This also gives an example of a nonassociative Moufang loop with a generating set in which every three elements have trivial associator.