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.
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Translated from Matematicheskie Zametki, Vol. 13, No. 3, pp. 443–446, March, 1973.
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Sesekin, N.F. On the product of finitely generated Abelian groups. Mathematical Notes of the Academy of Sciences of the USSR 13, 266–268 (1973). https://doi.org/10.1007/BF01155670
- Abelian Group
- Normal Subgroup
- Abelian Subgroup
- Nontrivial Normal Subgroup