[代數] cyclic group

看板Math作者 (無法顯示)時間12年前 (2011/09/04 22:14), 編輯推噓1(1推 0噓 6→)
留言7則, 3人參與, 最新討論串4/4 (看更多)
1. Let A = {x, a, b, c, d} (a) how many closed binary operations f on A satisfy f(a,b)=c 這個我知道是5^24 (b) how many of the functions f in part(a) have an identity? 3 * 5^15 (c) how many of the functions f in part(a) are commutative? 3 * 5^9 請問(b)跟(c)是為什麼? 2. Find all the elements of order 10 in (Z_40, +) 請問這題要怎麼找? 謝謝 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 61.228.25.26
推
09/04 22:27, , 1F
f has an identity? 什麼意思?
09/04 22:27, 1F
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09/04 22:45, , 2F
我是照題目打的 http://ppt.cc/e6vY
09/04 22:45, 2F
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09/04 22:57, , 3F
2. 根據條件知道 a≠1, b≠1
09/04 22:57, 3F
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09/04 23:18, , 4F
B)類似像這樣假設x是1 (a,?)=3,(b,?)=(c,?)=(d,?)=4
09/04 23:18, 4F
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09/04 23:19, , 5F
x,c,d都有可能所以乘3
09/04 23:19, 5F
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09/04 23:31, , 6F
f(x,s)=f(s,x)=s ,where s=a,b,c,d,x <=> x is an ID
09/04 23:31, 6F
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09/04 23:47, , 7F
因為f是函數所以f至多只有一個identity.(沒說明到)
09/04 23:47, 7F
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文章代碼(AID): #1EOuV65b (Math)
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文章代碼(AID): #1EOuV65b (Math)