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 . Finally some connections are mentioned between *SQ*-universality and the theory of ends.

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

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