Yan
Lv 5
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"

if and only if

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

3 個已更新項目:

4 個已更新項目:

5 個已更新項目:

### 1 個解答

• 9 年前
最佳解答

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