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serg [7]
2 years ago
11

LOOK FOR THE BEST THING EVER

Mathematics
1 answer:
Pie2 years ago
4 0

Answer:

look at this

Step-by-step explanation:

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Prove that H c G is a normal subgroup if and only if every left coset is a right coset, i.e., aH = Ha for all a e G
Kaylis [27]

\Rightarrow

Suppose first that H\subset G is a normal subgroup. Then by definition we must have for all a\in H, xax^{-1} \in H for every x\in G. Let a\in G and choose (ab)\in aH (b\in H). By hypothesis we have aba^{-1} =abbb^{-1}a^{-1}=(ab)b(ab)^{-1} \in H, i.e. aba^{-1}=c for some c\in H, thus ab=ca \in Ha. So we have aH\subset Ha. You can prove Ha\subset aH in the same way.

\Leftarrow

Suppose aH=Ha for all a\in G. Let h\in H, we have to prove  aha^{-1} \in H for every a\in G. So, let a\in G. We have that ha^{-1} =a^{-1}h' for some h'\in H (by the hypothesis). hence we have aha^{-1}=h' \in H. Because a was chosen arbitrarily  we have the desired .

 

5 0
3 years ago
Which of the point-slope equations below is correct for the line that passes through points (5,6) and (1,1)?
kherson [118]
It's y-6=5/4(x-5) which is C
6 0
3 years ago
19/23 Marks
PilotLPTM [1.2K]

Answer:

0.28

Step-by-step explanation:

Let p be the probability of pasta.

Total probability is = 1

Therefore,

0.3 + 0.42 + p = 1

0.72 + p = 1

p = 1 - 0.72

p = 0.28

The probability that it will be pasta is 0.28

4 0
3 years ago
Express 120% as a fraction in simplest form
Kisachek [45]

Answer:

6/5

Step-by-step explanation:

120% turns into 120/100 and from there you simply

3 0
3 years ago
Find the sum of 10 and the difference between 8 and 3
Bess [88]

Answer:

15

Step-by-step explanation:

10+(8-3)=15

................

3 0
2 years ago
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