Skip to main content
Log in

Subgroup separable free products with cyclic amalgamation

  • Article
  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

Using topological methods we give a proof that the free product of two strict subgroup separable groups with infinite cyclic amalgamation is subgroup separable.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Allenby, R. B. J. T. and Gregorac, R. J., ‘On locally extended residually finite groups’, Lecture Notes in Math., Springer-Verlag New York 319 (1973), 9–17.

    Article  MathSciNet  Google Scholar 

  2. Allenby, R. B. J. T. and Tang. C. Y., ‘Subgroup separability of generalized free products of free-by-finite groups’, Canad. Math. Bull., to appear.

  3. Brunner, A. M., Burns, R. G. and Solitar, D., ‘The subgroup separability of free products of two free groups with cyclic amalgamation’, Contemp. Math. 33 (1984), 90–115.

    Article  MathSciNet  Google Scholar 

  4. Burns, R. G., ‘On finitely generated subgroups of free products’, J. Austral. Math. Soc. 12 (1971), 358–364.

    Article  MathSciNet  MATH  Google Scholar 

  5. Gitik, R., ‘Graphs and LERF Groups’, preprint, Hebrew University, Jerusalem.

  6. Hall, M., Jr., ‘Coset representations in free groups’, Trans. Amer. Math. Soc. 67 (1949), 421–432.

    Article  MathSciNet  MATH  Google Scholar 

  7. Long, D. D. and Niblo, G. A., ‘Subgroup separability and 3-manifold groups’, Math. Z. 207 (1991), 209–215.

    Article  MathSciNet  MATH  Google Scholar 

  8. Malćev, A. I., ‘On homomorphisms onto finite groups’. Amer. Math. Soc. Transl. (2) 119 (1983), 67–79.

    Google Scholar 

  9. Niblo, G. A., ‘Fuchsian groups are strongly subgroup separable’, preprint, University of Sussex, 1989.

  10. Niblo, G. A., ‘H.N.N. extensions of a free group by Z which are subgroup separable’, Proc. London Math. Soc. (3) 61 (1990), 18–32.

    Article  MathSciNet  MATH  Google Scholar 

  11. Philpot, R. B., ‘Extensions of potent groups’, preprint (1983), Univ. of Melbourne.

  12. Rips, E., ‘An example of a non-LERF group which is a free product of LERF groups with an amalgamated cyclic subgroup’, Israel J. Math. 70 (1990), 104–110.

    Article  MathSciNet  MATH  Google Scholar 

  13. Scott, P., Correction to ‘Subgroups of surface groups are almost geometric’, J. London Math. Soc. (2) 32 (1985), 217–220.

    Article  MathSciNet  MATH  Google Scholar 

  14. Tang, C. Y., ‘On the subgroup separability of generalized free products of nilpotent groups’, Proc. Amer. Math. Soc. 113 (1991), 313–318.

    Article  MathSciNet  MATH  Google Scholar 

  15. Tretkoff, M., ‘Covering spaces, subgroup separability and the generalized M. Hall property’, Contemp. Math. 109 (1990), 179–191.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aab, M., Rosenberger, G. Subgroup separable free products with cyclic amalgamation. Results. Math. 28, 185–194 (1995). https://doi.org/10.1007/BF03322251

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03322251

1991 Mathematics subject classification

Keywords

Navigation