Geodesic
On the product of finitely generated Abelian groups
Matematičeskie zametki, Tome 13 (1973) no. 3, pp. 443-446 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is shown that if a group $G$ is a product of Abelian subgroups $A$ and $B$ one of which is finitely generated, then the group $G$ will have a nontrivial normal subgroup that is contained either in $A$, or in $B$. 
@article{MZM_1973_13_3_a14,
     author = {N. F. Sesekin},
     title = {On the product of finitely generated {Abelian} groups},
     journal = {Matemati\v{c}eskie zametki},
     pages = {443--446},
     year = {1973},
     volume = {13},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_13_3_a14/}
}
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N. F. Sesekin. On the product of finitely generated Abelian groups. Matematičeskie zametki, Tome 13 (1973) no. 3, pp. 443-446. http://geodesic.mathdoc.fr/item/MZM_1973_13_3_a14/