# Are Hyperbolic Groups Residually Amenable

It is a well-known conjecture (or maybe just a question) that all hyperbolic groups are residually finite. What happens if we weaken the conclusion; in particular

Are all hyperbolic groups residually amenable?

What is known in this direction?

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What are known examples of groups which are residually amenable but not residually finite? –  user15817 Jun 11 '13 at 14:41
Since f.g. Nilpotent groups are residually finite, at least residually nilpotent always implies residually finite. –  user15817 Jun 11 '13 at 14:44
@unknown(google): Baumslag solitar groups are residually solvable, hence residually amenable. Certain of these are not residually finite. –  Jon Bannon Jun 11 '13 at 14:52
@unknown: In the world of discrete groups;There are amenable groups that are not residually finite, take for example the wreath product $G\wr H$ with $G$ and $H$ amenable and $G$ non-abelian, (in fact there are also infinite and simple ones). As far as non-amenable examples, just take one of the examples above and then take a (direct or free) product with a residually finite non-amenable group (eg. $SL_n(\mathbb{Z})$. –  Owen Sizemore Jun 11 '13 at 14:54