A simple ballad Verfasser unbekannt; Quelle: Am. Math. Monthly, Nov. 1973 What are the orders of all simple groups? I speak of the honest onens, not of the loops. It seems that old Burnside their orders has guessed: except of the cyclic ones, even the rest. Groups made up with permutes will produce more: For A_n is simple, if n exceedes 4. Then, there was Sir Matthew who came into view exhibiting groups of an order quite new. Still others have come on the study this thing. Of Artin and Chevalley now shall sing. With matrices finite they made quite a list. The question is: Could there be others theve've missed? Suzuki and Ree then maintained it's the case that these methods had not reached the end of the chace. They wrote down some matrices, just four by four, that made up a simple group. Why not make more? And then came up the opus of Thompson and Feit which shed on the problem remarkable light. A group, when the order wont't factor by two, is cyclic or solvable. That's what true. Suzuki and Ree had caused eyebrows to raise, but the theoreticians they just couldn't face. Their groups were not new: if you added a twist, you could get them from old ones with a flick of the wrist. Still, some hardy souls felt a thorn in their side. For the five groups of Mathieu all reason defied: not A_n, not twisted, and not Chevaley. They called them sporadic and filed them away. Are Mathieu groups creatures of heaven or hell? Zvonimir Janko determinded to tell. He found out what nobody whanted to know: the masters had missed 1 7 5 5 6 0. The floodgates were opened) New groups were the rage! (And twelve or more sprouded, to great the new age.) By Janko and Conway and Fischer and Held, McLaughtin, Suzuki, and Higman, and Sims. No doubt you noted the last don't rhyme. Well, that is, quite simply, a sign of the time. There's chaos, not order, among simply groups, and maybe we'd better go back to the loops.