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

Info:

• Depth: 1
• Number of transitive dependencies: 1

Transitive dependencies:

1. Group