# Category:Quotient Theorem for Group Homomorphisms

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This category contains examples of use of Quotient Theorem for Group Homomorphisms.

Let $\phi: G \to G'$ be a (group) homomorphism between two groups $G$ and $G'$.

Then $\phi$ can be decomposed into the form:

- $\phi = \alpha \beta \gamma$

where:

- $\alpha: \Img \phi \to G'$ is a monomorphism
- $\beta: G / \map \ker \phi \to \Img \phi$ is an isomorphism
- $\gamma: G \to G / \map \ker \phi$ is an epimorphism.

## Pages in category "Quotient Theorem for Group Homomorphisms"

The following 6 pages are in this category, out of 6 total.

### Q

- Quotient Theorem for Group Homomorphisms
- Quotient Theorem for Group Homomorphisms/Examples
- Quotient Theorem for Group Homomorphisms/Examples/Inner Automorphism by Inverse Element
- Quotient Theorem for Group Homomorphisms/Examples/Integer Power on Circle Group
- Quotient Theorem for Group Homomorphisms/Examples/Integers to Modulo Integers under Multiplication
- Quotient Theorem for Group Homomorphisms/Examples/Real to Complex Numbers under e^2 pi i x