automorphic loop; semidirect product; middle nucleus; cyclic group
We analyze semidirect extensions of middle nuclei of commutative automorphic loops. We find a less complicated conditions for the semidirect construction when the middle nucleus is an odd order abelian group. We then use the description to study extensions of orders $3$ and $5$.
 Jedlička P., Simon D.: On commutative A-loops of order $pq$. to appear.