Isomorphism
An isomorphism is a bijective homomorphism ; in this case .
Definition 2.4 (Isomorphism)
If a homomorphism
is a bijection, then is an isomorphism. In this case, we write
From the perspective of group theory, isomorphic groups are considered the same.
Examples
The map with is an isomorphism. The exponential map is also an isomorphism, with inverse .
Related
Stated in
- Definition 2.4 (Isomorphism)§2.1 Introduction on Homomorphisms and Isomorphisms