# Thread: free abelian group as semi-direct products?

1. ## free abelian group as semi-direct products?

I have a HNN extension $G=$ where $A=L$ is a semi-direct product of $L$ by $$ and $$ is cyclic.

$G$ can be written as free products of $A$ and $B$ amalgamating $$ where $B=$ is a free abelian group.

Can $B$ expressed as a semi-direct product of cyclic free group $$ by $$?