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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- [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