Advertisement

Siberian Mathematical Journal

, Volume 54, Issue 3, pp 379–387 | Cite as

On the residual finiteness of generalized free products of finite rank groups

  • D. N. AzarovEmail author
Article

Abstract

We find necessary and sufficient conditions for the residual finiteness of some free products of finite rank groups with amalgamated subgroups.

Keywords

finite rank free product amalgamated subgroup residually finite group 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Hirsch K. A., “On infinite soluble groups,” J. London Math. Soc., 27, 81–85 (1952).MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Hsu T. and Wise D., “Ascending HNN extensions of polycyclic groups are residually finite,” J. Pure Appl. Algebra, 182, No. 1, 65–78 (2003).MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Baumslag G., “On the residual finiteness of generalized free products of nilpotent groups,” Trans. Amer. Math. Soc., 106, 193–209 (1963).MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Lennox J. and Robinson D., The Theory of Infinite Soluble Groups, Clarendon Press, Oxford (2004).zbMATHCrossRefGoogle Scholar
  5. 5.
    Shirvani M., “A converse to a residual finiteness theorem of G. Baumslag,” Proc. Amer. Math. Soc., 104, No. 3, 703–706 (1988).MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Lubotzky A. and Mann A., “Residually finite groups of finite rank,” Math. Proc. Cambridge Phil. Soc., 106, No. 3, 185–188 (1989).MathSciNetCrossRefGoogle Scholar
  7. 7.
    Dyer J., “On the residual finiteness of generalized free products,” Trans. Amer. Math. Soc., 133, No. 1, 131–143 (1968).MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Azarov D. N., “On almost residually p-finite groups,” Chebyshevskiĭ Sb., 11, No. 3, 11–21 (2010).Google Scholar
  9. 9.
    Mal’tsev A. I., “On homomorphisms onto finite groups,” Ivanovo Gos. Ped. Inst. Uchen. Zap., 18, No. 5, 49–60 (1958).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Ivanovo State UniversityIvanovoRussia

Personalised recommendations