Skip to main content
SpringerLink
Log in

On Solvable Groups with Proper Quotient Groups of Finite Rank

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We study solvable groups of infinite special rank all proper normal subgroups of which define quotient groups of finite special rank.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. D. J. S. Robinson and Z. Zang, “Groups whose proper quotients have finite derived subgroups,” J. Algebra, 118, 346–368 (1988).

    Google Scholar 

  2. D. J. S. Robinson and J. S. Wilson, “Soluble groups with many polycyclic quotients,” Proc. London Math. Soc., 48, No. 2, 193–229 (1984).

    Google Scholar 

  3. J. R. J. Groves, “Metabelian groups with finitely generated integral homology,” Quart. J. Math., 33, No. 2, 405–420 (1982).

    Google Scholar 

  4. A. V. Tushev, “On solvable groups all proper quotient groups of which have finite rank,” Ukr. Mat. Zh., 45, No. 3, 1274–1281 (1993).

    Google Scholar 

  5. A. V. Tushev, “On modules over metabelian groups of finite rank,” in: Abstracts of the International Conference on Algebra (Barnaul, August 1991) [in Russian], Barnaul (1991), p. 113.

  6. A. V. Tushev, “Induced modules over group algebra of metabelian groups of finite rank,” Commun. Algebra, 27, No. 12, 5921–5938 (1999).

    Google Scholar 

  7. A. V. Tushev, “On primitivity of group algebras of certain classes of solvable groups,” Mat. Sb., 186, No. 3, 143–160 (1995).

    Google Scholar 

  8. A. V. Tushev, “Spectra of conjugate ideals in group algebras of Abelian groups of finite rank and control theorems,” Glasgow Math. J., 38, 309–320 (1996).

    Google Scholar 

  9. A. V. Tushev, “On modules over groups rings of soluble groups of finite rank,” London Math. Soc. Lect. Note Ser., 261, 718–727 (1999).

    Google Scholar 

  10. D. I. Zaitsev, “Products of Abelian groups,” Algebra Logika, 19, No. 12, 150–172 (1980).

    Google Scholar 

  11. K. A. Brown, “The Nullstellensatz for certain group rings,” J. London Math. Soc., 26, 425–434 (1982).

    Google Scholar 

  12. V. S. Charin, “On groups of automorphisms of nilpotent groups,” Ukr. Mat. Zh., 6, No. 3, 295–304 (1954).

    Google Scholar 

  13. P. Hall, “Finiteness condition for soluble groups,” Proc. London Math. Soc., 4, No. 16, 419–436 (1954).

    Google Scholar 

  14. J. C. McConnell and J. C. Robson, Noncommutative Noetherian Rings, Wiley, New York (1987).

    Google Scholar 

  15. D. J. S. Robinson, A Course in the Theory of Groups, Springer, New York (1982).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dnepropetrovsk University, Dnepropetrovsk

    A. V. Tushev

Authors
  1. A. V. Tushev
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tushev, A.V. On Solvable Groups with Proper Quotient Groups of Finite Rank. Ukrainian Mathematical Journal 54, 1897–1905 (2002). https://doi.org/10.1023/A:1024052726835

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1024052726835

Keywords

Search

Navigation