10.3.14. Let G be a group of order 27. Let x Є G. Prove that x³ € Z(G).

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Answered: Let G be a group of order 27. Let x =…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.6: Quotient Groups

Problem 30E: Let G be a group with center Z(G)=C. Prove that if G/C is cyclic, then G is abelian.

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Let G be a group of order 27. Let x = G. Prove that x³ € Z(G).