On the SQ-universality of HNN groups

Fine, Benjamin; Tretkoff, Marvin

doi:10.1090/S0002-9939-1979-0518506-2

On the SQ-universality of HNN groups
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by Benjamin Fine and Marvin Tretkoff

Proc. Amer. Math. Soc. 73 (1979), 283-290

DOI: https://doi.org/10.1090/S0002-9939-1979-0518506-2

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Abstract:

A group G is SQ-universal if every countable group can be embedded in a quotient of G. In this paper we give conditions under which HNN groups are SQ-universal. These are then applied to showing the SQ-universality of certain classes of Kleinian groups (discontinuous subgroups of $PS{L_2}({\mathbf {C}})$. Finally some connections are mentioned between SQ-universality and the theory of ends.

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