Projection onto a quotient

#group_theory

Suppose $G$ is a group, $H$ and $K$ are normal subgroups of $G$ , and $H \leq K$ .
(a) Define a group homomorphism from $K$ to $G / H$ .
(b) Compute the kernel of the homomorphism in (a), and apply the First Isomorphism Theorem.

View

L A T E X

code

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}