Alternating bihomomorphism

Definition
Suppose $$G,H$$ are both subgroups of a group $$Q$$ and $$K$$ is a group. An alternating bihomomorphism is a set map $$b: G \times H \to K$$ that satisfies the following two conditions:


 * 1) $$b$$  is a bihomomorphism
 * 2) $$b(x,x)$$ is the identity element for any $$x \in G \cap H$$.