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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the SQ-universality of HNN groups

Authors: Benjamin Fine and Marvin Tretkoff
Journal: Proc. Amer. Math. Soc. 73 (1979), 283-290
MSC: Primary 20E34
MathSciNet review: 518506
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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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Keywords: SQ-universal, HNN group, generalized free product, Kleinian group, Fuchsian group, Klein's combination theorem, ends of a group
Article copyright: © Copyright 1979 American Mathematical Society

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