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!



Baumslag-Solitar subgroups of Poincare duality groups
The presentation complex of $BS(m,n)$ is aspherical (as is the presentation complex of any torsion-free 1-related group, see Lyndon and Schupp, ["Combinatorial group theory"](http://books.google.com/books?id=aiPVBygHi_oC&q=aspherical#v=snippet&q=aspherical&f=false), page 161). Hence by the [Davis construction](http://www.math.osu.edu/~mdavis/examples.pdf), $BS(m,n)$ embeds into the fundamental group of a closed aspherical 4-dim. manifold which is 
a  [PD group](http://www.math.osu.edu/~mdavis/pdgroup.pdf) . An explicit presentation of that bigger group may be not easy. 


