  Given a uniquely 2-divisible group $G$, we study a commutative loop
$(G,\circ)$ which arises as a result of a construction in \cite{baer}. We
investigate some general properties and applications of $\circ$ and determine a
necessary and sufficient condition on $G$ in order for $(G, \circ)$ to be
Moufang. In \cite{greer14}, it is conjectured that $G$ is metabelian if and
only if $(G, \circ)$ is an automorphic loop. We answer a portion of this
conjecture in the affirmative: in particular, we show that if $G$ is a split
metabelian group of odd order, then $(G, \circ)$ is automorphic.
