Prove that for each

.

I know that an automorphism sends a transposition to a transposition so is fine. How to prove the rest. I tried to use contradiction. denote . Assume . Then we should get a contradiction but i couldn't arrive at one.

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- Aug 14th 2011, 10:56 PMabhishekkgpautomorphisms of symmetric group.
Prove that for each

.

I know that an automorphism sends a transposition to a transposition so is fine. How to prove the rest. I tried to use contradiction. denote . Assume . Then we should get a contradiction but i couldn't arrive at one. - Aug 15th 2011, 12:38 AMabhishekkgpRe: automorphisms of symmetric group.
i just found something. let . Consider . So since is an isomorphism. Also . if are disjoint cycles then which is not possible. Hence there is one and only one element common in the cycles so WLOG . I guess this will prove the proposition. Please comment.