Residually finite $p$-groups of generalized free products of groups

Let $p$ be a prime number. Recall that a group $G$ is said to be a residually finite $p$-group if for every nonidentity element $a$ of $G$ there exists a homomorphism of the group $G$ onto some finite $p$-group such that the image of the element $a$ differs from unity. For the free product of two residually finite $p$-groups with amalgamated finite subgroups we obtain a necessary and sufficient condition to be a residually finite $p$-group. This result is a generalization of the similar Higman theorem proved for a free product of two finite $p$-groups with amalgamation.