Let φ : G → H be an onto homomorphism.(a) Assume that G is abelian. Does this imply that H is abelian? Whatabout the converse?(b) What if we replaced abelian by cyclic in the above question.

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Q: Needs Correct and complete explanation.     Don't use chat gpt or  ai i definitely upvote you

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A: We will find the solution of the given differential equations.

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A: answer is given below with explanation  p=xq=-2σ=1Explanation:Step 1: Step 2: Step 3: Step 4:

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A: The differential equation is :The aim is to solve the differential equation

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A: Proof are in explanation sectionExplanation:Step 1:

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A: ​(a) L−1{F(s)}=23​e25t​−(34sin(3t)​+2cos(3t))e2t​​(b)L−1{F(s)}=−e−2t+tet+2et​Explanation:Step 1: a.…

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Q: need help

A: The explanation of the answer is belowExplanation:Step 1: Step 2: Step 3: Step 4:

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Q: Plz solve correctly all parts Will definitely upvote

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A: (a) We have to calculate  where .in parametric form Now  and Now

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Q: Prove that this sequence is / is not Cauchy. xn + a xn+1 = xn-1

A: The proof is given in the explanation section.Explanation:Solution:A sequence xn​ is Cauchy if for…