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Let G be a group with the property that for any x, y, z in

Chapter 2, Problem 22E

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QUESTION:

Let G be a group with the property that for any x, y, z in the group, xy = zx implies y = z. Prove that G is Abelian. (“Left-right cancellation” implies commutativity.)

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QUESTION:

Let G be a group with the property that for any x, y, z in the group, xy = zx implies y = z. Prove that G is Abelian. (“Left-right cancellation” implies commutativity.)

ANSWER:

Step 1 of 3

Consider G be the group that has the property that for all . Then,

                           

 

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