Skip to main content
SpringerLink
Log in

Almost Hamiltonian Groups

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

In this paper we investigate the following problem in Group Theory: which properties $cal P$ transfer (or do not transfer) from all cyclic subgroups, or all abelian subgroups to all arbitrary subgroups? We solve this problem completely when $cal P$ is the property of having finite index in its normal closure, proving that $cal P$ carries from abelian, but not from cyclic to arbitrary subgroups. We use primarily some results of B.H. Neumann.

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. J. Buckley, J. C. Lennox, B. H. Neumann, H. Smith, and J. Wiegold, Groups with all subgroups normal-by-finite, J. Austral Math. Soc. Ser. A 59 (1995), 384–398.

    Article  MathSciNet  MATH  Google Scholar 

  2. S. Franciosi and F. de Giovanni, Groups with many normal-by-finite subgroups, Proc. AMS 125 (1997), 323–327.

    Article  Google Scholar 

  3. S. Franciosi, F. de Giovanni, and M. L. Newell, Groups whose subnormal subgroups are normal-by-finite, Comm. Algebra 23 (1995), 5483–5497.

    Article  MathSciNet  MATH  Google Scholar 

  4. F. de Giovanni and G. Vincenzi, Pronormality in infinite groups, Math. Proc. Royal Irish Acad. 100 (2000), 189–203.

    Google Scholar 

  5. B. H. Neumann, Groups with finite classes of conjugate subgroups, Math. Zeit. 63 (1955), 76–96.

    Article  MATH  Google Scholar 

  6. D. J. S. Robinson, A course in the theory of groups (2nd ed.), Graduate Texts in Mathematics 80, Springer-Verlag, New York, 1996.

  7. H. Smith and J. Wiegold, Locally graded groups with all subgroups normal-by-finite, J. Austral Math. Soc. Ser. A 60 (1996), 222–227.

    Article  MathSciNet  MATH  Google Scholar 

  8. N.F. Kuzenny>i and I. Ya. Subbotin, Groups in which all of the subgroups are pronormal (Russian), Ukrain. Mat. Zh. 39 (1987), 325–329, 405.

    MathSciNet  Google Scholar 

  9. I.Ya. Subbotin and N.F. Kuzenny>i, Locally solvable groups in which all infinite subgroups are pronormal (Russian), Izv. Vyssh. Uchebn. Zaved. Mat 1988, 77-79; Transi, in Soviet Math. (Iz. VUZ) 32 (1988), 126-131.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Auburn University Montgomery, P.O. Box 244023, Montgomery, AL 36124-4023, USA

    Tuval Foguel & Pantelimon Stănică

Authors
  1. Tuval Foguel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pantelimon Stănică
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tuval Foguel.

Additional information

Associated with the Institute of Mathematics “Simion Stoilow” of The Romanian Academy, Bucharest, Romania

Rights and permissions

Reprints and permissions

About this article

Cite this article

Foguel, T., Stănică, P. Almost Hamiltonian Groups. Results. Math. 48, 44–49 (2005). https://doi.org/10.1007/BF03322895

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03322895

2000 Mathematics Subject Classification

En]Keywords

Search

Navigation