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Let G be a group and define the map o : G → G by $(g) = g¬1. Show that o is an automorphism if and only if G is abelian.

Let G be a group and define the map o : G → G by $(g) = g¬1. Show that o is an automorphism if and only if G is abelian.

Elements Of Modern Algebra
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 and define the map o : G → G by $(g) = g¬1. Show that o is an automorphism if and only if G is abelian.
Transcribed Image Text:Let G be a group and define the map o : G → G by $(g) = g¬1. Show that o is an automorphism if and only if G is abelian.
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