Internal amalgamated free product

Definition
Suppose $$G$$ is a group and $$G_1$$ and $$G_2$$ are two subgroups of $$G$$ with intersection equal to a subgroup $$H$$. $$G$$ is an internal free product of $$G_1$$ and $$G_2$$ amalgamated at $$H$$ if the following condition is satisfied: given any word with the property that its letters alternate between $$G_1$$ and $$G_2$$, such that the word equals the identity element, all the elements of the word are from $$H$$.

The internal amalgamated free product of $$G_1$$ and $$G_2$$ over the subgroup $$H$$ is isomorphic to their external amalgamated free product.