# Math Help - Normal2

1. ## Normal2

Let G be a group. Every cyclic subgroup of G is normal, then prove that every subgroup of G is normal

2. Let $H$ be a subgroup of $G$, and let $g\in G,\ h\in H$. Then $\left$ is normal in $G$ and so $ghg^{-1}=h^n\in H$ for some $n\in\mathbb{Z}$. Hence $H\vartriangleleft G$