Factor Group

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Formal Definition

The group $G/H$ in Corollary 14.5 is the Factor Group(or quotient group) of $G$ by $H$

Informal Definition

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Since $\mathbb{Z}$ is an abelian group, $n\mathbb{Z}$ is a normal subgroup. Corollary 14.5 allows us to construct the factor group $\mathbb{Z}/n\mathbb{Z}$ with no reference to a homomorphism. $\mathbb{Z}/n\mathbb{Z}$ is isomorphic to $\mathbb{Z}_{n}$


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