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.
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.
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 aЄG, its inverse alpower{-1} is an automorphism
of G if any only if G is abelian.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fedde3d13-ac86-44a1-9b63-66e8ea5cf24d%2F72e933ce-461f-4a29-8ef6-21b4cb650156%2Fo1fc4u_processed.png&w=3840&q=75)
Transcribed Image Text:Let G be a group, then we have prove that a mapping which associates to
each element aЄG, its inverse alpower{-1} is an automorphism
of G if any only if G is abelian.
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