Theory: If G is a ﬁnite abelian group, p is prime and p divides the order of G then G has an element of order p.
Can anyone think of a counter example for a number n that is not prime, divides the order of some group, and the result proves its false.
I have looked at cyclic groups, the group of nth roots of unity and every finite abelian group I know, and no matter what, if some number divides the order of a group it has some element in it that has an order of that number. It doesn't really matter if it's prime or not. Any examples?