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 $x\in G\cap H$.