Skip to main content
SpringerLink
Log in

Residual finiteness, subgroup separability and conjugacy separability of certain HNN extensions

  • Regular Papers
  • Published:
Mathematica Slovaca

Abstract

In this note we shall give characterisations for HNN extensions of non-cyclic polycyclic-by-finite groups with normal infinite cyclic associated subgroups to be residually finite, subgroup separable and conjugacy separable.

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. ANDREADAKIS, S.— RAPTIS, E.— VARSOS, D.: A characterization of residually finite HNN-extensions of finitely generated abelian groups, Arch.Math. (Basel) 50 (1988), 495–501.

    Article  MathSciNet  MATH  Google Scholar 

  2. BAUMSLAG, G.— SOLITAR, D.: Some two-generator non-hopfian groups, Bull. Amer. Math. Soc. 68 (1962), 199–201.

    Article  MathSciNet  MATH  Google Scholar 

  3. BLACKBURN, N.: Conjugacy in nilpotent groups, Proc. Amer. Math. Soc. 16 (1965), 143–148.

    Article  MathSciNet  MATH  Google Scholar 

  4. COLLINS, D.: Recursively enumerating degree and the conjugacy problem, Acta. Math. 122 (1969), 115–160.

    Article  MathSciNet  MATH  Google Scholar 

  5. DYER, J. L.: Separating conjugates in amalgamatedfree products and HNN-extensions, J. Austral. Math. Soc. Ser. A 29 (1980), 35–51.

    Article  MathSciNet  MATH  Google Scholar 

  6. FINE, B.— ROSENBERGER, G.: Conjugacy separability of Fuchsian groups and related matters. Contemp. Math. 109, Amer. Math. Soc., Providence, RI, 1990, pp. 11–18.

    Google Scholar 

  7. FORMANEK, E.: Conjugate separability in polycylic groups, J. Algebra 42 (1976), 1–10.

    Article  MathSciNet  MATH  Google Scholar 

  8. HALL, M.: Coset representation in free groups, Trans. Amer. Math. Soc. 67 (1949), 421–432.

    Article  MathSciNet  MATH  Google Scholar 

  9. KIM, G.: Cyclic subgroup separability of HNN extensions, Bull. Korean Math. Soc. 30 (1993), 285–293.

    MathSciNet  Google Scholar 

  10. KIM, G.— TANG, C. Y.: Conjugacy separability of HNN-extensions of abelian groups, Arch. Math. (Basel) 67 (1996), 353–359.

    Article  MathSciNet  MATH  Google Scholar 

  11. KIM, G.— TANG, C. Y.: Cyclic subgroup separability of HNN extensions with cyclic associated subgroups, Canad. Math. Bull. 42 (1999), 335–343.

    Article  MathSciNet  MATH  Google Scholar 

  12. KIM, G.— TANG, C. Y.: A criterion for the conjugacy separability of certain HNN-extensions of groups, J. Algebra 222 (1999), 574–594.

    Article  MathSciNet  MATH  Google Scholar 

  13. KIM, G.— TANG, C. Y.: Conjugacy separability of certain HNN-extensions of groups, Rocky Mountain J. Math. 35 (2005), 587–601.

    Article  MathSciNet  MATH  Google Scholar 

  14. MAL’CEV, A.: On homomorphisms onto finite groups, Trans. Amer. Math. Soc. 119 (1983), 67–79.

    Google Scholar 

  15. METAFTSIS, V.— RAPTIS, E.: Subgroup separability of HNN extensions with abelian base group, J. Algebra 245 (2001), 42–49.

    Article  MathSciNet  MATH  Google Scholar 

  16. METAFTSIS, V.— RAPTIS, E.: Subgroup separability of graphs of abelian groups, Proc. Amer. Math. Soc. 132 (2004), 1873–1884.

    Article  MathSciNet  MATH  Google Scholar 

  17. NIBLO, G. A.: Separability properties of free groups and surface groups, J. Pure Appl. Algebra 78 (1992), 77–84.

    Article  MathSciNet  MATH  Google Scholar 

  18. REMESLENNIKOV, V. N.: Groups that are residually finitewith respect to conjugacy, Siberian Math. J. 12 (1971), 783–792.

    Article  MathSciNet  MATH  Google Scholar 

  19. SCOTT, P.: Subgroups of surface groups are almost geometric, J. London Math. Soc. 17 (1978), 555–565.

    Article  MathSciNet  MATH  Google Scholar 

  20. SCOTT, P.: Corrections to “Subgroups of surface groups are almost geometric”, J. London Math. Soc. 32 (1985), 217–220.

    Article  MathSciNet  MATH  Google Scholar 

  21. WONG, P. C.— WONG, K. B.: Subgroup separability and conjugacy separability of certain HNN extensions, Bull. Malays. Math. Sci. Soc. (2) 31 (2008), 25–33.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematical Sciences, University of Malaya, 50603, Kuala Lumpur, Malaysia

    K. B. Wong & P. C. Wong

Authors
  1. K. B. Wong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. C. Wong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. B. Wong.

Additional information

Communicated by Constantin Tsinakis

About this article

Cite this article

Wong, K.B., Wong, P.C. Residual finiteness, subgroup separability and conjugacy separability of certain HNN extensions. Math. Slovaca 62, 875–884 (2012). https://doi.org/10.2478/s12175-012-0052-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.2478/s12175-012-0052-7

2010 Mathematics Subject Classification

Keywords

Search

Navigation