Yan
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Yan 發問時間: 科學數學 · 9 年前

Normal subgroup?Factor group?

Give a group G under binary operation

If H is normal subgroup of G(i.e. Hg=gH for g∊G)

and G/H: (aH)(bH)=(ab)H for all a,b∊G

Show that "H is normal subgroup of G if and only if (aH)(bH)=(ab)H"

請問要如何證明粗體的部分?

已更新項目:

if and only if

所以請兩向都證明

2 個已更新項目:

Let H be a subgroup of a group G. Then left coset multiplication is well defined by the equation (aH)(bH)=(ab)H if and only if H is a normal subgroup of G

這是原來的題目

3 個已更新項目:

請問我有誤解錯誤嗎O_O?

4 個已更新項目:

請問為何(<= hH=H 我一直想不清楚

5 個已更新項目:

啊 我懂了~

1 個解答

評分
  • 9 年前
    最佳解答

    圖片參考:http://imgcld.yimg.com/8/n/AF03256679/o/1512020801...

    請參考,圖不清楚請下載至電腦

    2012-02-08 14:43:38 補充:

    hH=H是trivial不是嗎,就等同於我把群內的元素重新排過一遍而已= =

    Let H be a subgroup of a group G. Then left coset multiplication is "well defined" by the equation (aH)(bH)=(ab)H if and only if H is a normal subgroup of G

    有看到well define幾個字嗎

    參考資料: 我自己+數學娘的加持
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