Skip to main content
SpringerLink
Log in

The class of minimax groups is countably recognizable

  • Published:
Monatshefte für Mathematik Aims and scope Submit manuscript

Abstract

A class of groups is said to be countably recognizable if a group belongs to  whenever all its countable subgroups lie in . It is proved here that the class of minimax groups is countably recognizable.

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. Baer, R.: Abzählbar erkennbare gruppentheoretische Eigenschaften. Math. Z. 79, 344–363 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  2. Baer, R.: Polyminimaxgruppen. Math. Ann. 175, 1–43 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  3. Dixon, M.R., Evans, M.J., Smith, H.: Some countably recognizable classes of groups. J. Group Theory 10, 641–653 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  4. de Giovanni F., Trombetti M.: Countably recognizable classes of groups with restricted conjugacy classes. Int. J. Group Theory (to appear)

  5. de Giovanni F., Trombetti M.: Countable recognizability and nilpotency properties of groups. Rend. Circ. Mat. Palermo. (2016). doi:10.1007/s12215-016-0261-y

  6. Higman, G.: Almost free groups. Proc. Lond. Math. Soc. 1, 284–290 (1951)

    Article  MathSciNet  MATH  Google Scholar 

  7. Obraztsov, V.N.: An embedding theorem for groups and its corollaries. Math. USSR Sb. 66, 541–553 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  8. Phillips, R.E.: \(f\)-Systems in infinite groups. Arch. Math. (Basel) 20, 345–355 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  9. Phillips, R.E.: Countably recognizable classes of groups. Rocky Mt. J. Math. 1, 489–497 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  10. Robinson, D.J.S.: Finiteness conditions and generalized soluble groups. Springer, Berlin (1972)

    Book  MATH  Google Scholar 

  11. Smith, H.: More countably recognizable classes of groups. J. Pure Appl. Algebra 213, 1320–1324 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  12. Zaicev, D.I.: Groups which satisfy a weak minimality condition. Dokl. Akad. Nauk SSSR 178, 780–782 (1968)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Complesso Universitario Monte S. Angelo, Via Cintia, Napoli, Italy

    Francesco de Giovanni & Marco Trombetti

Authors
  1. Francesco de Giovanni
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marco Trombetti
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Francesco de Giovanni.

Additional information

Communicated by J. S. Wilson.

The authors are members of GNSAGA (INdAM), and work within the A\(_{\textstyle \mathrm{D}}\)V\(-{\textsc {AGTA}}\) project.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

de Giovanni, F., Trombetti, M. The class of minimax groups is countably recognizable. Monatsh Math 185, 81–86 (2018). https://doi.org/10.1007/s00605-016-0978-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00605-016-0978-x

Keywords

Mathematics Subject Classification

Search

Navigation