second isomorphism theorem

《The foundations of geometry》 · 第 262 页 · Section 11.5「Isomorphism Theorems」，Theorem 11.74

Theorem 11.74 (Second Isomorphism Theorem) Let $H$, $K$ be subgroups of a group $G$, and assume that $K$ is normal in $G$. Then $H/(H\cap K)\cong HK/K$. In fact, the function $H/(H\cap K)\to HK/K$ defined by $h(H\cap K)\mapsto hK$ is a well-defined isomorphism of groups.