Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

On the product of finitely generated Abelian groups

  • 36 Accesses

  • 2 Citations

Abstract

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.

This is a preview of subscription content, log in to check access.

Literature cited

  1. 1.

    N. Ito, “über das Produkt von zwei abelschen Gruppen,” Math. Z.,62, 400–401 (1955).

  2. 2.

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

  3. 3.

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

  4. 4.

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

  5. 5.

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

  6. 6.

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

  7. 7.

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

Download references

Author information

Additional information

Translated from Matematicheskie Zametki, Vol. 13, No. 3, pp. 443–446, March, 1973.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

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

Download citation

Keywords

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