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近世代数:设G为群,a,x∈G,证明:|a^-1|=|a|;|(x^-1)*a*x|=|a|
人气:380 ℃ 时间:2025-07-02 08:44:22
解答

|a|=p,
则a^-1^p=a^p^-1=e^-1=e因此|a^-1|=|a|
且((x^-1)*a*x)^p=(x^-1)*a*x (x^-1)*a*x.(x^-1)*a*x,即p个(x^-1)*a*x
=(x^-1)*a*(x(x^-1))*a*(x(x^-1))*a*x.=(x^-1)*a^p*x=(x^-1)*x=e后一个证毕

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