If G is a group and n>= 1, define G(n) = {x in G : ord(x) = n}

If G =~ H ( isomorphism ), show that for all n>= 1, |G(n)| = |H(n)|

deduce that C3* C3 is not isomorphic C9 ( where C3, C9 are the cyclic groups of order 3 and 9 respectively)

I have no clue how to do this question. Please help

Is it true that C3 * C5 =~ C15? I think the answer is YES because 3 and 5 are prime numbers, so the groups of these order are cyclic. Am I right?

Is it true that C2 * C6 =~ C12? I think not maybe because 6 is not a prime number.

Thank you for your time, I'm really appreciated