Group Homomorphism

definitiongroup-theory

Definition

A group homomorphism between two groups $(G,\cdot )$ and $(H,\ast )$ is a map $f:(G,\cdot )\to (H,\ast )$ such that for elements $x,y\in G$, $f(x\cdot y)=f(x)\ast f(y)$.

Types of Group Morphisms

• Isomorphism
• Automorphism

Examples