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user6976
user6976

If you mean action by automorphisms, then the answer is "no" since the Baumslag-Solitar groups $BS(m,n)$, $m\ne n\ge 2$$|m|\ne |n|\ge 2$ are not residually finite. The groups $BS(m,n)$ do act nicely on the products of a tree and the Hyperbolic space: http://www.emis.de/journals/JLT/13-2/galpl.ps.gz .

If you mean action by automorphisms, then the answer is "no" since the Baumslag-Solitar groups $BS(m,n)$, $m\ne n\ge 2$ are not residually finite. The groups $BS(m,n)$ do act nicely on the products of a tree and the Hyperbolic space: http://www.emis.de/journals/JLT/13-2/galpl.ps.gz .

If you mean action by automorphisms, then the answer is "no" since the Baumslag-Solitar groups $BS(m,n)$, $|m|\ne |n|\ge 2$ are not residually finite. The groups $BS(m,n)$ do act nicely on the products of a tree and the Hyperbolic space: http://www.emis.de/journals/JLT/13-2/galpl.ps.gz .

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user6976
user6976

If you mean action by automorphisms, then the answer is "no" since the Baumslag-Solitar groups $BS(m,n)$, $m\ne n\ge 2$ are not residually finite. The groups $BS(m,n)$ do act nicely on the products of a tree and the Hyperbolic space: http://www.emis.de/journals/JLT/13-2/galpl.ps.gz .