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.