TITLE: Is the Thompson Group F a subgroup of the Baumslag-Solitar group BS(2,1)?
QUESTION [5 upvotes]: The title pretty much sums it up : I'm wondering if BS(2,1) contains the Thompson Group F ?

REPLY [6 votes]: I think the answer is no. This probably isn't the easiest argument, but it's the first one that came to my mind:

Subgroups of residually finite groups are residually finite.
$BS(2,1)$ is residually finite (as every $B(m,n)$ with $m=1$ or $n=1$ or $m=n$).
Thompson's group $F$ isn't residually finite.