Skip to main content
SpringerLink
Log in

Groups with many normal or self-normalizing subgroups

  • Published:
Rendiconti del Circolo Matematico di Palermo Aims and scope Submit manuscript

Abstract

In this paper groups in which the set Σ of the normal or self-normalizing subgroups is large will be studied. In particular it will be characterized locally graded groups satisfying the minimal condition on subgroups which do not belong to Σ and locally finite groups for which the set Σ is dense in the lattice of all subgroups.

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. Amberg B., Franciosi S., de Giovanni F.,Products of Groups, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1992.

    MATH  Google Scholar 

  2. Brandl R., Franciosi S., de Giovanni F.,Groups with finitely many conjugacy classes of non-normal subgroups, Proc. Roy. Irish. Acad. 95A (1995), 17–27.

    Google Scholar 

  3. Černikov S. N.,Investigation of groups with given properties of the subgroups, Ukrain. Math. J.21 (1969), 160–172.

    Article  Google Scholar 

  4. Cutolo G.,A Normalizer Condition on Systems of Subgroups, Boll. Un. Math. Ital. (7)3-A (1989), 215–223

    MathSciNet  Google Scholar 

  5. Franciosi S., de Giovanni F.,Groups with dense normal subgroups, Ricerche Mat.42 (1993), 283–305.

    MATH  MathSciNet  Google Scholar 

  6. Franciosi S., de Giovanni F.,Groups satisfying the minimal condition on certain non-normal subgroups, Proceedings of “Groups-Korea 1994”, de Gruyter, Berlin (1995), 107–118.

    Google Scholar 

  7. Franciosi S., de Giovanni F.,Groups satisfying the minimal condition on non-subnormal subgroups, Proceedings of “Infinite Groups 1994”, de Gruyter, Berlin (1995), 63–72.

    Google Scholar 

  8. Giordano G.,Gruppi con normalizzatori estremali, Le Matematiche (Catania),26 (1971), 291–296.

    MathSciNet  Google Scholar 

  9. de Giovanni F., Vincenzi G.,Groups satisfying the minimal condition on non-pronormal subgroups, Boll. Un. Mat. Ital. (7)9A (1995), 185–194.

    Google Scholar 

  10. Mann A.,Groups with dense normal subgroups, Israel J. Math.6 (1968), 13–25.

    Article  MATH  MathSciNet  Google Scholar 

  11. Phillips R. E., Wilson J. S.,On certain minimal condition for infinite groups, J. Algebra51 (1978), 41–68.

    Article  MATH  MathSciNet  Google Scholar 

  12. Robinson D. J. S.,Finiteness Conditions and Generalized Soluble Groups, Springer, Berlin, 1972.

    Google Scholar 

  13. Šunkov V. P.,On locally finite groups with a minimality condition for abelian subgroups, Algebra and Logic9 (1970), 350–370.

    Article  Google Scholar 

  14. Smith H.,Groups with finitely many conjugacy classes of subgroups with large subnormal defect, Glasgow Math. J.37 (1995), 69–71.

    Article  MATH  MathSciNet  Google Scholar 

  15. Vincenzi G.,Groups with dense pronormal subgroups, Ricerche Mat.40 (1991), 75–79.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica ed Applicazioni, Università di Napoli “Federico II”, Complesso Universitario Monte S. Angelo, Via Cintia 1, 80126, Napoli, (Italy)

    Annalisa Galoppo

Authors
  1. Annalisa Galoppo
    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

Galoppo, A. Groups with many normal or self-normalizing subgroups. Rend. Circ. Mat. Palermo 47, 397–408 (1998). https://doi.org/10.1007/BF02851388

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02851388

Keywords

Search

Navigation