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. 
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     author = {N. S. Romanovskii},
     title = {Finite approximabiliyt of free products with respect to occurrence},
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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/

[1] Kargapolov M. I., Merzlyakov Yu. I., Beskonechnye gruppy, Itogi nauki. Algebra. Topologiya. Geometriya. 1966, Moskva, 1968 | MR | Zbl

[2] Maltsev A. I., “O gomomorfizmakh na konechnye gruppy”, Uch. zap. Ivanovsk. ped. in-ta, 18 (1958), 49–60

[3] Hall M., “Coset representations in free groups”, Trans. Amer. Math. Soc., 67 (1949), 421–432 | DOI | MR | Zbl

[4] Magnus W., Karras A., Solitar D., Combinatorial group theory, New York, London, Sydney, 1966 | MR

[5] Mikhailova K. A., “Problema vkhozhdeniya dlya svobodnogo proizvedeniya grupp”, Matem. sb., 75:2 (1968), 199–211 | MR

[6] Gruenberg K. W., “Residual properties of infinite soluble groups”, Proc. Lond. Math. Soc., VII:25 (1957), 29–62 | DOI | MR

[7] Romanovskii N. S., “O finitnoi approksimiruemosti svobodnykh proizvedenii otnositelno vkhozhdeniya”, Algebra i logika, 7:5 (1968), 3 | MR