Category:Definitions/Group Homomorphisms

This category contains definitions related to Group Homomorphisms.
Related results can be found in Category:Group Homomorphisms.

Let $\struct {G, \circ}$ and $\struct {H, *}$ be groups.

Let $\phi: G \to H$ be a mapping such that $\circ$ has the morphism property under $\phi$.

That is, $\forall a, b \in G$:

$\map \phi {a \circ b} = \map \phi a * \map \phi b$

Then $\phi: \struct {G, \circ} \to \struct {H, *}$ is a group homomorphism.