Geodesic
Homomorphic images of Abelian groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 3, pp. 17-24
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For some classes of Abelian groups, we answer the question of when a union of homomorphic images of a group is a subgroup of another group. In connection with this, the concept of a homomorphically stable group is introduced and properties of homomorphically stable groups from different classes of Abelian groups are studied. 
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S. Ya. Grinshpon; T. A. Yeltsova. Homomorphic images of Abelian groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 3, pp. 17-24. http://geodesic.mathdoc.fr/item/FPM_2007_13_3_a2/

[1] Fuks L., Beskonechnye abelevy gruppy, T. 1, Mir, M., 1974

[2] Fuks L., Beskonechnye abelevy gruppy, T. 2, Mir, M., 1977