# Tag Info

## Hot answers tagged normal-subgroups

Neither of your characterisations of normal subgroup are correct. You should re-read whatever sources you are using carefully. A subgroup $H$ of $G$ is normal if and only if for all $h \in H$, for ...
### $K \unlhd A \rightarrow \Phi(A)$ is isomorphism
There is 1-1 correspondence between $\{ A\leq G_1 : K\leq A\}$ and subgroups of $\pi (G_1) = G_1 / K$. surjective: as $\pi$ is surjective, for every subgroups $C \leq G_1 / K$ exists \$\pi ^ {-1} (C) \...