“Feit–Thompson conjecture”的意思、由来-开放百科全书

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Feit–Thompson conjecture

释义

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In mathematics, the Feit–Thompson conjecture is a conjecture in number theory, suggested by {{harvs|txt=yes|first=Walter|last= Feit|authorlink=Walter Feit| first2=John G. |last2=Thompson|author2-link=John G. Thompson|year=1962}}. The conjecture states that there are no distinct prime numbers p and q such that

divides .

If the conjecture were true, it would greatly simplify the final chapter of the proof {{harv|Feit|Thompson|1963}} 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 {{harvtxt|Stephens|1971}} with the counterexample p = 17 and q = 3313 with common factor 2pq + 1 = 112643.

It is known that the conjecture is true for q = 3 {{harv|Le|2012}}.

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.

References

{{citation

}} {{MathSciNet|id=0143802}}

{{citation

| last= Feit|first=Walter|last2=Thompson|first2= John G.
| title = Solvability of groups of odd order
| journal = Pacific J. Math.
| volume = 13
| year = 1963
| pages = 775–1029
| issn = 0030-8730
| doi = 10.2140/pjm.1963.13.775
| mr = 0166261
}}

{{citation

| last= Le|first=Mao Hua
| title = A dibisibility problem concerning group theory
| journal = Pure Appl. Math. Q.
| volume = 8
| year = 2012
| pages = 689–691
| issn = 1558-8599
| doi = 10.4310/PAMQ.2012.v8.n3.a5
| mr = 2900154
}}

{{citation

| last = Stephens
| first = Nelson M.
| title = On the Feit–Thompson conjecture
| journal = Math. Comp.
| volume = 25
| year = 1971
| pages = 625
| doi = 10.2307/2005226
| jstor=2005226
| mr = 0297686
}}

External links

{{MathWorld|urlname=Feit-ThompsonConjecture|title=Feit–Thompson Conjecture}} (This article confuses the Feit–Thompson conjecture with the stronger disproved conjecture mentioned above.)

2 : Conjectures|Number theory

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