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:

$\phi = \alpha \beta \gamma$


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