Dupe of big FAQ on the hot network list, with (poor) dupe answer by high rep user. Of course the fact that cyclic groups satisfy the converse of Lagrange's theorem is proved in
many prior answers. Not clear how to best handle this, but I think we should do all we can to discourage such duplicate answers (esp. by frequent offenders), since linking to prior answers will yield much richer knowledge for the questioner. Any group theorists here?