A. What is the order of ([15]20 , [20]24) in Z20 × Z24?B. What is the largest order of an element in Z20 × Z24? And use your answer to show that Z20 × Z24is not cyclic.C. Let G =Zo x Zo10'10Let H = ((3, 7)) and K= ((7, 7))Find HK in GHere, (3, 7) means ([3]10: [7]10)Just use this simplified notations in your answer.

Answered: Image /qna-images/answer/294b8b51-ae88-422d-9c84-a1d52805d5e2.jpg

A. What is the order of ([15]20, [20]24) in Z20 × Z24? B. What is the largest order of an element in Z20 × Z24? And use your answer to show that Z20 × Z24 is not cyclic. C. Let G= Z10 × Zîo Let H = ((3, 7)) and K = ((7, 7)) Find HK in G Here, (3, 7) means ([3]10- [7]10) Just use this simplified notations in your answer.

A. What is the order of ([15]20, [20]24) in Z20 × Z24? B. What is the largest order of an element in Z20 × Z24? And use your answer to show that Z20 × Z24 is not cyclic. C. Let G= Z10 × Zîo Let H = ((3, 7)) and K = ((7, 7)) Find HK in G Here, (3, 7) means ([3]10- [7]10) Just use this simplified notations in your answer.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.3: The Characteristic Of A Ring

Problem 13E

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