Second isomorphism theorem for groups
= Second isomorphism theorem for groups
{title2=$H/(H\cap N)\cong HN/N$}
For a <subgroup> $H\leq G$ and a <normal subgroup> $N\trianglelefteq G$, the map $h\mapsto hN$ from $H$ onto $HN/N$ is a <group homomorphism> with kernel $H\cap N$. The <first isomorphism theorem> gives the displayed <group isomorphism>. The product $HN$ is a <subgroup> because $N$ is normal. In particular, if $HN=G$ and $H\cap N=1$, then $H\cong G/N$.