Let $H:=\mathbb{Z}*\mathbb{Z}/n\mathbb{Z}=\langle p,q| q^n=1\rangle.$ I want to know if $H$ is a ($\mathbb{Z}$)linear group that is to say is there an injective homomorphism $f: H\to GL_m(\mathbb{Z})$ for $m\geq n.$
I asked the question on Math Stack Exchange (https://math.stackexchange.com/questions/1430677/is-the-free-product-mathbbz-mathbbz-n-mathbbz-a-linear-group) and Derek Holt suggested me to also ask it here.
By advance thank you.