[代數] 想請問一題代數

看板Math作者 (Banana)時間9年前 (2016/12/06 19:04), 編輯推噓0(004)
留言4則, 2人參與, 最新討論串1/1
Assume that G is a finite group, and let H be a nonempty subset of G. Prove that H is closed if and only if H is subgroup of G. (<=) Since H is subgroup of G, H is closed. (=>) Since H is closed and nonempty set. 存在一個 a 屬於 H, a*a 屬於 H 接下來就不知道怎麼找出 e 了... 謝謝 -- ※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 122.116.58.245 ※ 文章網址: https://www.ptt.cc/bbs/Math/M.1481022275.A.229.html

12/06 19:14, , 1F
利用 finite,a*a*...*a 乘夠多次一定會出現重複
12/06 19:14, 1F

12/06 19:14, , 2F
所以存在 m>n 使得 a^m = a^n
12/06 19:14, 2F

12/06 19:14, , 3F
因此 a^(m-n)=e
12/06 19:14, 3F

12/06 19:45, , 4F
謝謝 kkagt
12/06 19:45, 4F
文章代碼(AID): #1OHfj38f (Math)