On the splitting of groups of central group extensions

It is proved that if $G$ and $V$ are abelian groups, sthen the group $\operatorname{Ext}(G, V)$ of all abelian extensions of the group $V$ with the aid of the group $G$ is extracted by the direct component in the group $\operatorname{Opext}(G,V)$ of all central extensions of $V$ with the aid of $G$.