  Let $Q$ be a conjugacy closed loop, and $N(Q)$ its nucleus. Then $Z(N(Q))$
contains all associators of elements of $Q$. If in addition $Q$ is
diassociative (i.e., an extra loop), then all these associators have order 2.
If $Q$ is power-associative and $|Q|$ is finite and relatively prime to 6, then
$Q$ is a group. If $Q$ is a finite non-associative extra loop, then $16 \mid
|Q|$.
