Inverse of a group isomorphism is a group isomorphism

Dependencies:

1. Isomorphism on Groups

Inverse of a bijection is a bijection, so $\phi^{-1}$ is a bijection.

Let $x = \phi(a), y = \phi(b)$.

$\phi(ab) = \phi(a)\phi(b) \Rightarrow \phi^{-1}(x)\phi^{-1}(y) = \phi^{-1}(xy)$.

Therefore, $\phi^{-1}$ is an isomorphism.

Dependency for:

1. Isomorphism of groups is an equivalence relation

Info:

• Depth: 2
• Number of transitive dependencies: 2

Transitive dependencies:

1. Group
2. Isomorphism on Groups