Odd-order and CN implies solvable

Statement
Any uses property satisfaction of::odd-order group that is also a   CN-group (and hence a uses property satisfaction of::finite CN-group) must be a   proves property satisfaction of::solvable group (and hence, a proves property satisfaction of::finite solvable group).

Note that the odd-order theorem says that every odd-order group is solvable, and therefore, this result is too weak to be of any use beyond what the odd-order theorem already tells us. However, it is a lot easier to prove than the odd-order theorem, and its utility lies in the way it helps pave the way for a proof of the odd-order theorem.