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This question already has an answer here:

I'm asked to write out the cycle decomposition of each element of order 2 in $S_4$. However, from my understanding, a cycle decomposition is the product of disjoint cycles. But the elements in $S_4$ of order 2 are already products of disjoint cycles. For example,

How do I simplify (1 2) or (1 2)(3 4)?

Isn't the only way to write (1 2) as a product (1 2)=(1 2)(1 2)? Which is not disjoint and hence not a cycle decomposition? And isn't (1 2)(3 4) already a cycle decomposition?

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marked as duplicate by Daniel W. Farlow, Namaste group-theory Oct 6 '16 at 0:11

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It sounds like the question is looking for you to identify the ones which are of order 2. It's more of an identification problem and not a decomposition problem.

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