Say we have a finite Moufang Loop $Q$, $|Q|<\infty$.

There is a theorem proved by Thompson that states:

Group $G$, $|G|<\infty$ is solvable $\iff$ $\forall a, b \in G \langle a, b\rangle$ is solvable.

My question is: can we translate the theorem to the finite Moufang loops (may be with some extra constraints)?

The statement is reasonable because it is well-known that every pair of Moufang loop's elements forms a group structure (Moufang's theorem).

What is interesting, Feit–Thompson theorem about solvability of finite groups with odd order translates to the Moufang loop case. The proof can be found here.

There is an idea to translate the task to the case of $U(R)$, where $R$ is alternative algebra, $1 \in R$.