the Odd Order Theoremはこれか？ 有名なFeit–Thompson theorem：有限単純群の位数は偶数でなければならない。 en.wikipedia.org/wiki/Feit%E2%80%93Thompson_theorem In mathematics, the Feit–Thompson theorem, or odd order theorem, states that every finite group of odd order is solvable. It was proved by Walter Feit and John Griggs Thompson (1962, 1963)
The Feit–Thompson theorem can be thought of as the next step in this process: they show that there is no non-cyclic simple group of odd order such that every proper subgroup is solvable. This proves that every finite group of odd order is solvable, as a minimal counterexample must be a simple group such that every proper subgroup is solvable. Although the proof follows the same general outline as the CA theorem and the CN theorem, the details are vastly more complicated. The final paper is 255 pages long.
Revision of the proof Many mathematicians have simplified parts of the original Feit–Thompson proof. However all of these improvements are in some sense local; the global structure of the argument is still the same, but some of the details of the arguments have been simplified.
The simplified proof has been published in two books: (Bender & Glauberman 1995), which covers everything except the character theory, and (Peterfalvi 2000, part I) which covers the character theory. This revised proof is still very hard, and is longer than the original proof, but is written in a more leisurely style.
A fully formal proof, checked with the Coq proof assistant, was announced in September 2012 by Georges Gonthier and fellow researchers at Microsoft Research and INRIA.[1]
