Prove that Zn Zn is notisomorphic to any subgroup of Zm for any m.
1 answer:
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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Answer:
Rational Function
Step-by-step explanation:
Gives the function:
It has the following,
Domain
x∈ :
Range
End behaviour
As x
Horizontal and Vertical Asymptote
Vertical
Horizontal
<em>x-intercept: (2,0)</em>
<em>y-intercept: none</em>
<em>**The Graph is in the annex</em>
