ABSTRACT
We call a group homomorphism an isomorphism if it is a one-to-one and onto function. Intuitively, a group isomorphism preserves all essential group theoretic properties, and so demonstrates that two groups are ‘essentially the same’. If ϕ : G → H is a group isomorphism between the groups G and H, the inverse function ϕ−1 : H → G is also a group isomorphism.
