I have recently studying Tits' alternative. The theorem statement goes like the following: **Tits' alternative:** Let $G$ be any finitely generated linear group over a field. Then one of the following is true, $(1)$ $G$ contains a solvable normal subgroup of finite index, $(2)$ $G$ contains a non-abelian free subgroup (of rank at least $2$). I am in search of applications of this wonderful theorem in algebraic number theory. Any help, resources or reference will be appreciated. Thanks in advance.