Skip to main content
Log in

On abelian groups with right-invariant isometries

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

We describe the reduced periodically complete groups, algebraically compact groups, and torsion-free completely decomposable groups with right-invariant monomorphisms preserving the p-heights of the elements of the group under study.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Monk G. S., “Abelian p-groups without proper isomorphic pure dense subgroups,” Illinois J. Math., 14, No. 1, 164–177 (1970).

    MATH  MathSciNet  Google Scholar 

  2. Beaumont R. A. and Pierce R. S., “Isomorphic direct summands of abelian groups,” Math. Ann., 153, 21–37 (1964).

    Article  MathSciNet  Google Scholar 

  3. Goldsmith B., Óhógáin S., and Wallutis S., “Quasi-minimal Abelian groups,” Proc. Amer. Math. Soc., 132, No. 8, 2185–2195 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  4. Pierce R. S., “Homomorphisms of primary abelian groups,” in: Topics in Abelian Groups (Proc. Sympos., New Mexico State Univ., 1962), Scott, Foresman and Co., Chicago, Ill., 1963, pp. 215–310.

    Google Scholar 

  5. Grinshpon S. Y. and Nikolskaya M. M., “Fully invariant subgroups of abelian p-groups with finite Ulm-Kaplansky invariants,” Comm. Algebra, 39, No. 11, 4273–4282 (2011).

    Article  MATH  MathSciNet  Google Scholar 

  6. Chekhlov A. R., “Abelian groups with normal endomorphism rings,” Algebra and Logic, 48, No. 4, 298–308 (2009).

    Article  MATH  MathSciNet  Google Scholar 

  7. Călugăreanu G. and Schultz Ph., “Modules with Abelian endomorphism rings,” Bull. Austral. Math. Soc., 82, No. 1, 99–112 (2010).

    Article  MATH  Google Scholar 

  8. Chekhlov A. R., “E-solvable modules,” J. Math. Sci. (New York), 183, No. 3, 424–434 (2012).

    Article  MATH  Google Scholar 

  9. Chekhlov A. R., “On Abelian groups close to E-solvable groups,” J. Math. Sci. (New York), 197, No. 5, 708–733 (2014).

    Article  MathSciNet  Google Scholar 

  10. Chekhlov A. R., “Abelian groups with nilpotent commutators of endomorphisms,” Russian Math. (Iz. VUZ), 56, No. 10, 50–61 (2012).

    MATH  MathSciNet  Google Scholar 

  11. Chekhlov A. R., “On direct sums of cyclic groups with invariant monomorphisms,” Vestnik Tomsk Gos. Univ. Math. Mekh., No. 3, 60–65 (2013).

    Google Scholar 

  12. Chekhlov A. R., “On abelian groups with commuting monomorphisms,” Siberian Math. J., 54, No. 5, 946–950 (2013).

    Article  MATH  MathSciNet  Google Scholar 

  13. Kylikov L. Ya., “On the theory of Abelian groups of arbitrary power,” Mat. Sb., 16, No. 4, 129–162 (1945).

    Google Scholar 

  14. Mishina A. P., “On automorphisms and endomorphisms of abelian groups,” Vestnik Moskov. Univ. Ser. I Mat. Mekh., No. 4, 39–43 (1962).

    Google Scholar 

  15. Krylov P. A., “Extension of isomorphisms in abelian p-groups,” Math. Notes, 14, No. 4, 870–872 (1973).

    Article  Google Scholar 

  16. Fuchs L., “Extensions of isomorphisms between subgroups,” Lecture Notes in Math., 874, 289–296 (1981).

    Article  Google Scholar 

  17. Chistyakov D. S. and Lyubimtsev O. V., “Abelian groups as endomorphic modules over their endomorphism ring,” J. Math. Sci. (New York), 152, No. 4, 604–607 (2008).

    Article  MATH  MathSciNet  Google Scholar 

  18. Tuganbaev A. A., “Automorphisms of submodules and their extensions,” Discrete Math. Appl., 25, No. 1, 115–124 (2013).

    MathSciNet  Google Scholar 

  19. Fuchs L., Infinite Abelian Groups. Vol. 1 and 2, Academic Press, New York and London (1970, 1973).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. R. Chekhlov.

Additional information

Original Russian Text Copyright © 2014 Chekhlov A.R.

__________

Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 55, No. 3, pp. 701–705, May–June, 2014.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chekhlov, A.R. On abelian groups with right-invariant isometries. Sib Math J 55, 574–577 (2014). https://doi.org/10.1134/S0037446614030185

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0037446614030185

Keywords

Navigation