Prove: that $H$ is a normal subgroup of $G$.

Question

Let $G$ be a group, any cyclic subgroup of $G$ is normal in $G$, and $H$ any subgroup of $G$. Prove that $H$ is a normal subgroup of $G$.

possible duplicate of If every cyclic subgroup of $G$ is normal so is every subgroup? — Dietrich Burde, Jun 25 '14 at 19:40

score 4 · Answer 1 · answered Jun 25 '14 at 19:37

4

Pretty straightforward: $$ H=\bigcup_{h\in H}\langle h \rangle $$ (the conclusion is left to the reader ;)

answered Jun 25 '14 at 19:37

String

1 Answers1