[代數] 幾題關於group的證明@@
以下(G,*,e)為一群，想證 j
-1 r j -j r
(1) if a, b∈G, b*a*b = a , then b * a * b = a for some r∈Ｎ
這題想不出來啊...想用數學歸納法， k
k+1 -(k+1) k -k -1 r
可是b *a*b 頂多拆b(b * a * b )b 然後中間卡一個a ....
(2) │G│ is finite, H is a subset of G, prove that H is a subgroup of G
if and only if e∈H and a*b∈H for all a, b∈G
不會證inverse∈H的部分@@
(3) H, K are subgroup of G, prove that if H∪K is a subgroup of G,
then H⊆K or K⊆H
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