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.