My awesome math prof posted a practice midterm but didn't post any solutions to it :s Here is the question.
Let $G$ be a group and let $H$ be a subgroup of $G$.
- (a) TRUE or FALSE: If $G$ is abelian, then so is $H$.
- (b) TRUE or FALSE: If $H$ is abelian, then so is $G$.
Part (a) is clearly true but I am having a bit of difficulty proving it, after fulling the conditions of being a subgroup the commutative of $G$ should imply that $ab=ba$ somehow.
Part (b) I am fairly certain this is false and I know my tiny brain should be able to find an example somewhere but it is 4 am here :) I want to use some non-abelian group $G$ then find a generator to make a cyclic subgroup of $G$ that is abelian.
Any help would be appreciated, I have looked in my book but I can't seem to find for certain what I am looking for with what we have cover thus far.