Prove that a group G is Abelian iff .
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We have Then the equality becomes . Multiply both sides at left by : Now, multiply both sides by If G as abelian the identity is obvious:
I don't understand how you get as I have in the problem. What allows you to switch them as we are proving the group is communtative, and not assuming it is. (From my understanding)
Originally Posted by tttcomrader I don't understand how you get as I have in the problem. What allows you to switch them as we are proving the group is communtative, and not assuming it is. (From my understanding) is an element such that when multiplied by produces (identity). Since it means .
Thank you, sir, it is clear now.
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