# Category:Group Isomorphisms

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This category contains results about **Group Isomorphisms**.

Let $\struct {G, \circ}$ and $\struct {H, *}$ be groups.

Let $\phi: G \to H$ be a (group) homomorphism.

Then $\phi$ is a group isomorphism if and only if $\phi$ is a bijection.

## Subcategories

This category has the following 9 subcategories, out of 9 total.

### E

### G

### I

### P

## Pages in category "Group Isomorphisms"

The following 32 pages are in this category, out of 32 total.

### G

### I

- Infinite Cyclic Group is Unique up to Isomorphism
- Inner Automorphism Group is Isomorphic to Quotient Group with Center
- Internal and External Group Direct Products are Isomorphic
- Internal Group Direct Product Isomorphism
- Inverse of Group Isomorphism is Isomorphism
- Inversion Mapping is Isomorphism from Ordered Abelian Group to its Dual
- Isomorphism of Abelian Groups
- Isomorphism of Finite Group with Permutations of Quotient with Subgroup