Group Homomorphism Preserves Identity/Proof 2
Jump to navigation
Jump to search
Theorem
Let $\struct {G, \circ}$ and $\struct {H, *}$ be groups.
Let $\phi: \struct {G, \circ} \to \struct {H, *}$ be a group homomorphism.
Let:
Then:
- $\map \phi {e_G} = e_H$
Proof
A direct application of Homomorphism to Group Preserves Identity.
$\blacksquare$
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {II}$: New Structures from Old: $\S 12$: Homomorphisms