Can a Poincaré duality group $G$ contain Baumslag--Solitar subgroups $H$ such as BS(1,3) or BS(2,3)?
I don't mean to include those subgroups which are the fundamental group of the torus or Klein bottle. Also, one can show that index must be infinite: $[G:H] = \infty$.
If so, what is a simple example of such $G$ and $H$?
In any case, please let me know of references. Thanks!