Geodesic
Finite approximabiliyt of free products with respect to occurrence
Izvestiya. Mathematics , Tome 3 (1969) no. 6, pp. 1245-1249

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We shall say that a group $G$ belongs to a class $\Phi\mathrm{AB}_\omega$ if and only if for any finitely generated subgroup $H$ of $G$ and any element $g$ of $G$ that does not lie in $H$ there exists a homomorphism of $G$ into a finite group such that the image of $g$ does not belong to the image of the subgroup $H$. We prove that the class $\Phi\mathrm{AB}_\omega$ is closed under the operation of free multiplication. 
@article{IM2_1969_3_6_a4,
     author = {N. S. Romanovskii},
     title = {Finite approximabiliyt of free products with respect to occurrence},
     journal = {Izvestiya. Mathematics },
     pages = {1245--1249},
     publisher = {mathdoc},
     volume = {3},
     number = {6},
     year = {1969},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1969_3_6_a4/}
}
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N. S. Romanovskii. Finite approximabiliyt of free products with respect to occurrence. Izvestiya. Mathematics , Tome 3 (1969) no. 6, pp. 1245-1249. http://geodesic.mathdoc.fr/item/IM2_1969_3_6_a4/