Geodesic
$\operatorname{IA}$-Automorphisms of Free Products of Two Abelian Torsion-Free Groups
Matematičeskie zametki, Tome 70 (2001) no. 6, pp. 909-917 
P. V. Ushakov. $\operatorname{IA}$-Automorphisms of Free Products of Two Abelian Torsion-Free Groups. Matematičeskie zametki, Tome 70 (2001) no. 6, pp. 909-917. http://geodesic.mathdoc.fr/item/MZM_2001_70_6_a8/
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     author = {P. V. Ushakov},
     title = {$\operatorname{IA}${-Automorphisms} of {Free} {Products} of {Two} {Abelian} {Torsion-Free} {Groups}},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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