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Irina18 [472]
3 years ago
8

Prove that Zn Zn is notisomorphic to any subgroup of Zm for any m.

Mathematics
1 answer:
WINSTONCH [101]3 years ago
5 0

Answer and Step-by-step explanation:

Every group homomorphism ϕ:Zn→Zm extends in a unique way to a linear transformation T:Qn→Qm of vector spaces over Q.

Moreover, ϕ is injective iff T is injective. But T being injective implies n≤m.

Applying this to both ϕ and ϕ−1, we conclude that n≤m≤n.

NOTE:

The proof and step-by-step explanation is in the attachment below

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<em>I </em><em>hope </em><em>it </em><em>will </em><em>useful</em>

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2 years ago
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3 years ago
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8 0
3 years ago
Can someone please help me with question 35?
Genrish500 [490]
First you would find the area of the triangle which would be 84×92 then divide that answer by 2.
Then you will find the area of the circle using the given radius 20.5.
Lets work it out.
84×92=7728
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A=pi(20.5)²
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3864-1320.25=2543.75 ft²
2543.75 ft² is your answer.
Hope This Helps and God Bless!
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