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On the product of finitely generated Abelian groups

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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.

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Literature cited

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    P. Cohn, “A remark on the general product of two infinite cyclic groups,” Arch. Math.,7, No. 2, 94–99 (1956).

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    N. F. Sesekin, “On the product of finitely connected Abelian groups,” Sibirsk. Matem. Zh., No. 6, 1427–1429 (1968).

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    W. R. Scott, “On a result of Schenkman on product of Abelian groups,” Notices Amer. Math. Soc.,16, 796 (1969), Abst. 667–737.

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    E. Schenkman, “The general product of two finitely generated Abelian groups,” Proc. Amer. Math. Soc.,21, 202–204 (1969).

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    B. Amberg and W. Scott, “Products of Abelian subgroups,” Proc. Amer. Math. Soc.,26, 541–547 (1970).

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    D. J. S. Robinson, “A theorem on finitely generated hyperabelian groups,” Inventiones Math.,10, No. 1, 38–43 (1970).

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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).

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  • Abelian Group
  • Normal Subgroup
  • Abelian Subgroup
  • Nontrivial Normal Subgroup