Feit-Thompson conjecture

The Feit-Thompson conjecture is a number theoretical conjecture that would simplify the proof of the Feit-Thompson theorem and thus the classification of the finite simple groups considerably.

The conjecture states that there is no prime numbers and with there, for by divisible is. ${\displaystyle p}$ ${\displaystyle q}$ ${\displaystyle p\not =q}$ ${\displaystyle {\frac {q^{p}-1}{q-1}}}$ ${\displaystyle {\frac {p^{q}-1}{p-1}}}$

An original, stronger version of the conjecture said that and for every two prime numbers and with are coprime . However, this stronger version is wrong, it is the simplest counterexample . ${\displaystyle {\frac {q^{p}-1}{q-1}}}$ ${\displaystyle {\frac {p^{q}-1}{p-1}}}$ ${\displaystyle p}$ ${\displaystyle q}$ ${\displaystyle p\not =q}$ ${\displaystyle p=17,q=3313}$

literature

• Feit, Walter; Thompson, John G. (1962), "A solvability criterion for finite groups and some consequences", Proc. Natl. Acad. Sci. USA, 48 (6): 968-970
• Feit, Walter; Thompson, John G. (1963), "Solvability of groups of odd order", Pacific J. Math., 13: 775-1029

Web links

• Feit-Thompson Conjecture (MathWorld)

Individual evidence

1. ↑ Stephens, Nelson M. (1971), "On the Feit-Thompson conjecture," Math. Comp., 25: 625