Let G=A^{\; *}_{H} A be the generalized free products amalgamating H. Let G be residually finite. How to show that A is H-separable?
I'm sure that A must be H-separable. But I don't know how to show this.
I started with x \in A \backslash H.
Since A is residually finite, then there exists M \lhd_{f} A such that x \notin M.
I'm trying to prove by contradiction, by assuming x \in HM.
How can I continue from here?