5.(a) Ifp is a prime then the group U, has o (d) elementsof order d for each d dividing p- 1.(b) If n= rs where r and s are coprime and are bothgreater than 2, then prove that U, is not cyclic.

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Answered: 5. (a) Ifp is a prime then the group U,…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.4: Cosets Of A Subgroup

Problem 27E: Prove that any group with prime order is cyclic.

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5. (a) Ifp is a prime then the group U, has (d) elements of order d for each d dividing p- 1. (b) Ifn = rs where r and s are coprime and are both greater than 2, then prove that U, is not cyclic.