hey, G is a group such that o(G) = 36. Then is G abelian.
I knw that if o(G) = p^2 where p is a prime, then G is abelian. But here
o(G)=2^2 * 3^2. So what can I say about G.
This is no pre-university math.
Observe that G has sylow-p subgroups $\displaystyle |H_1|= 3^2, |H_2| = 2^2$, which are as you stated abelian.
Since both groups are abelian we have $\displaystyle H_1 \triangleleft G$ and $\displaystyle H_2 \triangleleft G$. Now it follows that $\displaystyle G \cong H_1\times H_2$. ( trivially it follows that G is abelian)