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Homethird isomorphism theorem

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# third isomorphism theorem

If $G$ is a group (or ring, or module) and $H$ and $K$ are normal subgroups (or ideals, or submodules, respectively) of $G$, with $H\subseteq K$, then there is a natural isomorphism $(G/H)/(K/H)\cong G/K$.

This is usually known either as the Third Isomorphism Theorem, or as the Second Isomorphism Theorem (depending on the order in which the theorems are introduced). It is also occasionally called the Freshman Theorem.

Synonym:

freshman theorem

Type of Math Object:

Theorem

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

20A05*no label found*13A15

*no label found*16D10

*no label found*

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