Sometimes, groups are more than just similar. If they are identical, they are isomorphic. Isomorphism is comprised of two Greek words that mean equal and form. In mathematics, isomorphism is a perfect one-to-one, bijective mapping between two groups (structures or sets). Every object in group A maps directly to an object in group B.
In an isomorphism, every object in A is mapped to an object in B. The morphisms are also injective because no two objects from A map to the same object in B. So, if the objects in A are x, y, and z, then the following are not possible: f(x) = f(y), f(x) = f(z), f(y) = f(z). The only mappings we find ...
