Bihomomorphism

Definition with symbols
Let $$G,H,K$$ be groups. A map $$f:G \times H \to K$$ is termed a bihomomorphism if for every $$g$$ in $$G$$, the induced map $$h \mapsto f(g,h)$$ is a homomorphism from $$H$$ to $$K$$, and for every $$h \in H$$, the induced map $$g \mapsto f(g,h)$$ is a homomorphism from $$G$$ to $$K$$.

Bihomomorphism is a group-theoretic variant of the notion of bilinear map in vector spaces.