# Section9.2The Second and Third Isomorphism Theorems

The following theorems can be proven using the First Isomorphism Theorem. They are very useful in special cases.

##### Example9.2.3

Using the Third Isomorphism Theorem, we see that the group

\begin{equation*} (\Z/12\Z)/(6\Z/12\Z) \end{equation*}

is isomorphic to the group $\Z/6\Z\text{,}$ or $\Z_6\text{.}$