Let alpha and beta belong to S_n. Prove that (beta)(alpha)(beta^-1) and alpha are both even or both odd.
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Originally Posted by mandy123 Let alpha and beta belong to S_n. Prove that (beta)(alpha)(beta^-1) and alpha are both even or both odd. Notice that . Therefore if where are transpositions then . Thus, we see that and have the same parity.
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