扁頭科學 asked in 科學數學 · 9 years ago

代數normal subgroup的證明

1.If N⊳G and H is a subgroup of G, show that H∩N⊳H.

2.If Φ is an automorphism of G and N⊳G, then prove that Φ(N)⊳G.

2 Answers

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  • 9 years ago
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    圖片參考:http://imgcld.yimg.com/8/n/AF03256679/o/1511112414...

    至於第二題....

    http://tw.knowledge.yahoo.com/question/question?qi...

    跟這題不是一樣的嗎?

    或者說你問的這題條件更強

    把證明稍微改過就OK了,麻煩請自行修正

    2011-11-24 22:31:22 補充:

    你要不要加都沒差啦

    我覺得那邊都很明顯了,但為了避免老師D掉,你還是加一下比較好

    最後一行你說的沒錯,那是打錯字了,請修正

    Source(s): 我自己+數學娘的加持
  • 9 years ago

    1第一行consider that hxh^-1後面是不是應該加上h∈H and H a subgroup of G,

    所以h∈G,且x∈N,和N⊳G,所以hxh^-1∈N

    2第三行next後面,為甚麼要加上H<=G,不是因為h,x∈H再根據群的乘法封閉性就可以了嗎

    3第四行應該是for all x∈H∩N吧

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