w Let G be a group, then we have prove that a mapping which associates toeach element aЄG, its inverse alpower{-1} is an automorphismof G if any only if G is abelian.

Given :Let G be a group and a is element of G .To prove : we have prove that a mapping which…

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Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.2: Properties Of Group Elements

Problem 16E: Suppose ab=ca implies b=c for all elements a,b, and c in a group G. Prove that G is abelian.

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Let G be a group, then we have prove that a mapping which associates to each element aĒG, its inverse a\power{-1} is an automorphism of G if any only if G is abelian.