103 5 5. Let G be a group and let's choose an element g € G. Show that the map o, : G → G defined by,(h) = ghg-1 for all h e G is a homomorphism.

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Answered: 5. Let G be a group and let's choose an…

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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5. Let G be a group and let's choose an element g € G. Show that the map Óg : G → G defined by 0g(h) = ghg¬1 for all h e G is a homomorphism. %3D