Could somebody please help me prove the following two statements:
- Any subgroup $H$ of a soluble group is itself soluble.
- If $G$ is soluble and $N$ is normal in $G$ then $G/N$ is soluble.
- I know we can consider the subnormal series of $G$ intersect $H$, but then why is each factor normal in the last and abelian?
- No idea
Thanks for any help!