I'm helping a friend with a problem that I can't figure out. I would appreciate some guide lines on how to tackle this:

__Prove__: Every finite group is a disjoint union of cyclic subgroups.

If a group is Abelian, this should be a restatement of the Fundamental Theory of Finite Abelian Groups. I also know that the dihedral groups

satisfies the requirements for this statement. But how do we tackle the case when we have a general group

that is not abelian?

I would appreciate any help that you're able to give.