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 P S L 2 ( C ) PS{L_2}({\mathbf {C}}) . Finally some connections are mentioned between SQ-universality and the theory of ends.
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