Abelianness is invariant under isomorphism

Dependencies:

1. Isomorphism on Groups

If $G \cong H$ and $G$ is abelian, then $H$ is abelian.

Proof

Let $\phi(a), \phi(b) \in H$. Then $\phi(a)\phi(b) = \phi(ab) = \phi(ba) = \phi(b)\phi(a)$.

Dependency for: None

Info:

• Depth: 2
• Number of transitive dependencies: 2

Transitive dependencies:

1. Group
2. Isomorphism on Groups