# Category:Group Epimorphisms

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

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

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

Then $\phi$ is a group epimorphism if and only if $\phi$ is a surjection.

## Subcategories

This category has the following 4 subcategories, out of 4 total.

## Pages in category "Group Epimorphisms"

The following 26 pages are in this category, out of 26 total.

### E

### G

- Group Epimorphism Induces Bijection between Subgroups
- Group Epimorphism Induces Bijection between Subgroups/Corollary
- Group Epimorphism is Isomorphism iff Kernel is Trivial
- Group Epimorphism preserves Central Subgroups
- Group Epimorphism Preserves Generator
- Group Epimorphism Preserves Normal Subgroups
- Group Epimorphism Preserves Subgroups

### P

- Power Function on Complex Numbers is Epimorphism
- Preimage of Image of Subgroup under Group Epimorphism
- Preimage of Normal Subgroup of Quotient Group under Quotient Epimorphism is Normal
- Preimage of Normal Subgroup under Epimorphism is Normal Subgroup
- Preimage of Subgroup under Epimorphism is Subgroup
- Projection on Group Direct Product is Epimorphism