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G, ba = ca implies b = c and ab = ac implies b = c for elements a, b, c E G. 31. Show that if a? = e for all elements a in a group G, then G must be abelian.

G, ba = ca implies b = c and ab = ac implies b = c for elements a, b, c E G. 31. Show that if a? = e for all elements a in a group G, then G must be abelian.

Elements Of Modern Algebra
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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G, ba = ca implies b = c and ab = ac implies b = c for elements a, b, c E G. 31. Show that if a? = e for all elements a in a group G, then G must be abelian. 32. Show that if G is a finite group of even order, then there is an a E G such that a is not
Transcribed Image Text:G, ba = ca implies b = c and ab = ac implies b = c for elements a, b, c E G. 31. Show that if a? = e for all elements a in a group G, then G must be abelian. 32. Show that if G is a finite group of even order, then there is an a E G such that a is not
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