In order to prove something is a subgroup of $G$, you must prove it is a group - one of which criteria is that it is associative. Any tips for proving associativity in these situations? I'm thinking saying something like:
Fix arbitrary $a,b,c$ are in $H$. Then they must be in $G$ since they are in $H$. Since $G$ is associative, $(ab)c = a(bc)$. So $H$ is associative.
Is this sufficient? By the way, this is for an undergrad Modern Algebra course.