Israel Journal of Mathematics

, Volume 85, Issue 1–3, pp 11–18 | Cite as

Some remarks on profinite HNN extensions



We extend a construction of Higman, Neumann and Neumann [LS, IV.3.1] and show that every profinite groupG with only countably many open subgroups embeds in a 2-generated profinite groupE in which all torsion elements are conjugate to elements ofG; ifG is pro-p,E can be chosen pro-p. This answers a question of Wilson (oral communication) and generalises a result of Lubotzky and Wilson [LW].


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  1. [BT] B. Baumslag and M. Tretkoff,Residually finite HNN extensions, Comm. Alg.6 (1978), 179–194.MATHCrossRefMathSciNetGoogle Scholar
  2. [GR] D. Gildenhuys and L. Ribes,Profinite groups and Boolean graphs, Journal of Pure and Applied Algebra12 (1978), 21–47.MATHCrossRefMathSciNetGoogle Scholar
  3. [H] G. Higman,Amalgams of p-Groups, Journal of Algebra1 (1964), 301–305.MATHCrossRefMathSciNetGoogle Scholar
  4. [LW] A. Lubotzky and J. S. Wilson,An embedding theorem for profinite groups, Arch. Math.42 (1984), 397–399.MATHCrossRefMathSciNetGoogle Scholar
  5. [LS] R. C. Lyndon and P. E. Schupp,Combinatorial Group Theory, Springer, Berlin, 1977.MATHGoogle Scholar
  6. [M] O. V. Mel'nikov,Normal subgroups of free profinite groups, Izv. Akad. Nauk. SSSR Ser. Mat.42 (1978), 3–25; English transl. in Math. USSR Izv.12 (1978), 1–20.MATHMathSciNetGoogle Scholar
  7. [R] L. Ribes,On amalgamated products of profinite groups, Math. Z.123 (1971), 357–364.CrossRefMathSciNetGoogle Scholar
  8. [ZM1] P. A. Zalesskii and O. V. Mel;nikov,Subgroups of profinite groups acting on trees, Mat. Sbornik135 (177) (1988), No 4, 419–439; Engl. transl. in Math USSR Sbornik63 (1989), No 2, 405–424.Google Scholar
  9. [ZM2] P. A. Zalesskii and O. V. Mel'nikov,Fundamental groups of graphs of profinite groups, Algebra i Analiz1 (1989), 117–135; Engl. Transl. in Leningrad Math. J.1 (1990), 921–940.MathSciNetGoogle Scholar

Copyright information

© Hebrew University 1994

Authors and Affiliations

  1. 1.UFR de MathematiquesUniversité de Paris 7Paris Cedex 05France

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