23/01/31 15:55:49.87 tkHk7/Du.net
>>75
>ガロアより以前に置換群論において正規部分群という概念を思いついた
>という人は居ないのだろうか?
ガロアは、Chevallierへの手紙(下記)で
・正規部分群について明記している
(This is called proper decomposition:G = H + H S + H S' + ・・とG = H +TH +T'H +・・とが一致するとき)
・”If each of these groups has a prime number of permutations then the equation will be solvable by radicals; otherwise, not.”と明記している
・The smallest number of permutations that an indecomposable group can have,when this number is not a prime number, is 5・4・3.(=位数60のA5(交代群))と明記している
Chevallierへの手紙は、明らかにガロア理論の創始!
(これより以前は、アーベルの方程式論が最前線です)
(参考)
>>90より
URLリンク(www.ias.ac.in)
The Last Mathematical Testament of Galois
Evariste Galois's last mathematical testament in the form ofa letter to his friend Auguste Chevallier is
reproduced here in English translation I.
P1
The second contains rather interesting applications from the theory of equations.Here is a summary of the most important ones:
1. According to the propositions II and III of the first paper, one sees a great difference between adjoining, to an equation, . one of the roots or all the roots of an auxiliary equation.
つづく