Results in Mathematics

, Volume 28, Issue 3–4, pp 185–194 | Cite as

Subgroup separable free products with cyclic amalgamation

  • Michael Aab
  • Gerhard Rosenberger
Article

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.

1991 Mathematics subject classification

57M07 20E07 57M10 

Keywords

Subgroup separability Free products with amalgamation 

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References

  1. [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.MathSciNetCrossRefGoogle Scholar
  2. [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.Google Scholar
  3. [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.MathSciNetCrossRefGoogle Scholar
  4. [4]
    Burns, R. G., ‘On finitely generated subgroups of free products’, J. Austral. Math. Soc. 12 (1971), 358–364.MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    Gitik, R., ‘Graphs and LERF Groups’, preprint, Hebrew University, Jerusalem.Google Scholar
  6. [6]
    Hall, M., Jr., ‘Coset representations in free groups’, Trans. Amer. Math. Soc. 67 (1949), 421–432.MathSciNetMATHCrossRefGoogle Scholar
  7. [7]
    Long, D. D. and Niblo, G. A., ‘Subgroup separability and 3-manifold groups’, Math. Z. 207 (1991), 209–215.MathSciNetMATHCrossRefGoogle Scholar
  8. [8]
    Malćev, A. I., ‘On homomorphisms onto finite groups’. Amer. Math. Soc. Transl. (2) 119 (1983), 67–79.Google Scholar
  9. [9]
    Niblo, G. A., ‘Fuchsian groups are strongly subgroup separable’, preprint, University of Sussex, 1989.Google Scholar
  10. [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.MathSciNetMATHCrossRefGoogle Scholar
  11. [11]
    Philpot, R. B., ‘Extensions of potent groups’, preprint (1983), Univ. of Melbourne.Google Scholar
  12. [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.MathSciNetMATHCrossRefGoogle Scholar
  13. [13]
    Scott, P., Correction to ‘Subgroups of surface groups are almost geometric’, J. London Math. Soc. (2) 32 (1985), 217–220.MathSciNetMATHCrossRefGoogle Scholar
  14. [14]
    Tang, C. Y., ‘On the subgroup separability of generalized free products of nilpotent groups’, Proc. Amer. Math. Soc. 113 (1991), 313–318.MathSciNetMATHCrossRefGoogle Scholar
  15. [15]
    Tretkoff, M., ‘Covering spaces, subgroup separability and the generalized M. Hall property’, Contemp. Math. 109 (1990), 179–191.MathSciNetCrossRefGoogle Scholar

Copyright information

© Birkhäuser Verlag, Basel 1995

Authors and Affiliations

  • Michael Aab
    • 1
  • Gerhard Rosenberger
    • 1
  1. 1.Fachbereich MathematikUniversität DortmundDortmund

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