青ㄟ
Lv 6
青ㄟ asked in 科學數學 · 1 decade ago

代數學-Prove or Disprove

Let G be a group of finite number of elements.Then ,for any a€G, there exists an n€Z+(正整數) such that a^n=e

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  • 1 decade ago
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    設 G 有 k 個元素, 則 a^1=a, a^2, a^3,...,a^{k+1} 必有兩者杷同,

    設 a^r = a^s 其中 r≠s. 設 r>s, 因 a^s 有反元素, 故得 a^{r-s}=e.

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