Isomorphism on Groups

Dependencies:

1. Group

Groups $G_1$ and $G_2$ are isomorphic ($G \cong H$) iff there is a bijection $\phi$ from $G_1$ to $G_2$ such that $\phi(ab) = \phi(a)\phi(b)$. $\phi$ is called an isomorphism.

Dependency for:

1. Cyclic groups are isomorphic to Z or Zn
2. Cyclicness is invariant under isomorphism
3. Cayley's Theorem
4. Zm × Zn is isomorphic to Zmn iff m and n are coprime
5. Order of elements is invariant under isomorphism
6. Isomorphism of groups is an equivalence relation
7. Inverse of a group isomorphism is a group isomorphism
8. Abelianness is invariant under isomorphism

Info:

• Depth: 1
• Number of transitive dependencies: 1

Transitive dependencies:

1. Group