Answer to Question #188454 in Abstract Algebra for akshat

Question #188454

If (a,b) E AxA, where A is a group, then o((a,b))=o(a)o(b)

Expert's answer

Let "A" be a group. If "o(a)=o(b)=2", then "(a,b)(a,b)=(a^2,b^2)=(1_A,1_A)", and hence "o((a,b))=2". It follows that in general case it is not true that "o((a,b))=o(a)o(b)."

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