$\operatorname{IA}$-Automorphisms of Free Products of Two Abelian Torsion-Free Groups

Let $A$ be the free product of two Abelian torsion-free groups, let $P\triangleleft A$ and $P\subseteq C$, where $C$ is the Cartesian subgroup of the group $A$, and let $\mathbb Z(A/P)$ contain no zero divisors. In the paper it is proved that, in this case, any automorphism of the group $A/P'$ is inner. This result generalized the well-known result of Bachmuth, Formanek, and Mochizuki on the automorphisms of groups of the form $F_2/R'$, $R\triangleleft F_2$, $R\subseteq F'_2$, where $F_2$ is a free group of rank two.