Projection onto a quotient
Suppose
- Define a group homomorphism from
to . - Compute the kernel of the homomorphism in (a), and apply the First Isomorphism Theorem.
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Suppose $G$ is a group, $H$ and $K$ are normal subgroups of $G$, and $H\leq K$.
\begin{enumerate}[label=\alph*)]
\item Define a group homomorphism from $K$ to $G/H$.
\item Compute the kernel of the homomorphism in (a), and apply the First Isomorphism Theorem.
\end{enumerate}