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You are not logged in. #1 20090520 02:48:48
The Feit–Thompson theoremOkay, I only just found out what it is. All groups of odd order are soluble (or solvable). Let be a finite group of composite odd order (so it’s soluble by Feit–Thompson). We may assume that is not Abelian, since we all know that any Abelian group of composite order is not simple. Since it is not Abelian, its derived subgroup is not trvial. Also cannot be all of otherwise for all whereas being soluble means that must be trivial after a finite number of derivations. Hence the commutator subgroup of is a nontrivial and proper normal subgroup, proving that is not simple. There. That was not really heavy machinery, was it? #2 20090520 03:06:40
Re: The Feit–Thompson theorem
That solvability of composite order implies nonsimplicity is not, no. In fact, it becomes more obvious when you use the decomposition series that comes from being solvable. On the other hand, FeitThompson's theorem required 255 pages of heavy machinery to prove. I'm not sure of any proofs discovered since then, so perhaps it has become shorter with time. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #3 20090520 03:14:34
Re: The Feit–Thompson theorem
Oh, that puts a different complexion on the matter then. #4 20090520 05:54:45
Re: The Feit–Thompson theoremThought I read about a 1000 page proof in group theory. Andy's is 200, this is 250. What ever happened to the Greeks drive for simplicity? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #5 20090520 06:44:07
Re: The Feit–Thompson theoremThe first half of the JordanHolder program is estimated at 10,000 pages. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." 