Thread: Cycle decomposition in Sn

This question is most likely about a problem I am misinterpreting.

Show that an element has order 2 in $\displaystyle S_n$ iff its cycle decomposition is a product of commuting 2-cycles.

Now as far as I can tell this problem is talking about elements of $\displaystyle S_n$ like (12)(34). But $\displaystyle S_2 < S_n$. What about elements such as (12)? Or am I being too picky about having to have at least 2 2-cycles?

-Dan

Yes, one cycle is treated as a product of one factor.