Feit–Thompson Proof
Feit–Thompson may refer to: * Feit–Thompson conjecture * Feit–Thompson 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 . History conjectured that every nonabelian finite simple group has even order. suggested using th ... {{disambiguation ...
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Feit–Thompson Conjecture
In mathematics, the Feit–Thompson conjecture is a conjecture in number theory, suggested by . The conjecture states that there are no distinct prime numbers ''p'' and ''q'' such that :\frac divides \frac. If the conjecture were true, it would greatly simplify the final chapter of the proof of the Feit–Thompson theorem that every finite group of odd order is solvable. A stronger conjecture that the two numbers are always coprime was disproved by with the counterexample ''p'' = 17 and ''q'' = 3313 with common factor 2''pq'' + 1 = 112643. It is known that the conjecture is true for ''q'' = 3 . Informal probability arguments suggest that the "expected" number of counterexamples to the Feit–Thompson conjecture is very close to 0, suggesting that the Feit–Thompson conjecture is likely to be true. See also *Cyclotomic polynomials *Goormaghtigh conjecture In mathematics, the Goormaghtigh conjecture is a conjectur ...
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