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抄點(diǎn)不會(huì)的楊子胥抽代習(xí)題Day0

2023-02-17 21:00 作者:RIP_Official  | 我要投稿


證明:設(shè)x%2Cy%5Cin%20G,有%5Cvarphi(xy)%3D%5Cvarphi(x)%5Cvarphi(y)%5Cvarphi(yx)%3D%5Cvarphi(y)%5Cvarphi(x).

(xy)%5E3%3Dx%5E3y%5E3%0A(yx)%5E3%3Dy%5E3x%5E3,

進(jìn)而(yx)%5E2%3Dx%5E2y%5E2(xy)%5E2%3Dy%5E2x%5E2,

同理(y%5E2x%5E2)%5E2%3Dx%5E4y%5E4%2C

考慮(xy)%5E4%3D((xy)%5E2)%5E2%3D(y%5E2x%5E2)%5E2%3Dx%5E4y%5E4

從而(yx)%5E3%3Dx%5E3y%5E3,即%5Cvarphi(xy)%3D%5Cvarphi(yx),由%5Cvarphi%0A單,知道xy%3Dyx%0A,即證.? ? ? ? ? ? ??

證明:設(shè)%5Cvarphi%5Cin%20C(%7B%5Crm%20Aut%7DG),%5Cphi_a%3Ax%5Cto%20a%5E%7B-1%7Dxa%5Cin%5Crm%20InnG.

于是%5Cvarphi%5Cphi_a%3D%5Cphi_a%5Cvarphi,即

%5Cvarphi(a%5E%7B-1%7Dxa)%3Da%5E%7B-1%7D%5Cvarphi(x)%20a,%5Cforall%20x%5Cin%20G.

這樣%5Cvarphi(a)%5E%7B-1%7D%5Cvarphi(x)%5Cvarphi(a)%3Da%5E%7B-1%7D%5Cvarphi(x)a,從而%5Cvarphi(a)a%5E%7B-1%7D%5Cvarphi(x)%3D%5Cvarphi(x)%5Cvarphi(a)a%5E%7B-1%7D,

于是由%5Cvarphi(x)任意性知道%5Cvarphi(a)%3Da,由a任意性知道%5Cvarphi%3D%5Crm%20Id.

?第二個(gè)做的時(shí)候單純地想到了InnG了,但是不知道和AutG搞在一起,完全不知道,總感覺(jué)有某些神奇手段避免和InnG接觸,看了答案之后也不清楚為啥這樣.這樣不會(huì)那也忘了,寄了。

抄點(diǎn)不會(huì)的楊子胥抽代習(xí)題Day0的評(píng)論 (共 條)

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