In finite groups e = a^n for every a

Dear reader, I wrote this so long ago, I am even too lazy to follow this. You may disregard this post.

I wanted to prove it, so I did. Being bad with mathematical induction is also among the reasons. The proof includes tons of gory details, which to me were the most interesting part of this endeavour. Fortunately, the proof of |C| + 1 <= |G| has been left out.