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Math Help - Cycle decomposition in Sn

  1. #1
    Forum Admin topsquark's Avatar
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    Cycle decomposition in Sn

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

    Show that an element has order 2 in 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 S_n like (12)(34). But 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
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    Re: Cycle decomposition in Sn

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