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Math Help - infinite cycles in Sym(N)

  1. #1
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    Question infinite cycles in Sym(N)

    I need an example of two infinite cycles in Sym(N) which are not conjugate.(N is the set of natural numbers)
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  2. #2
    Senior Member jakncoke's Avatar
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    Re: infinite cycles in Sym(N)

    I'm also interested in how you classify conjugancy classes on infinite cycles.
    Last edited by jakncoke; February 26th 2013 at 09:43 AM.
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  3. #3
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    Re: infinite cycles in Sym(N)

    Two permutations x,y \in Sym(\Omega) are conjugate in Sym(\Omega) iff they have the same number of cycles of each type (including 1-cycles).
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  4. #4
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    Re: infinite cycles in Sym(N)

    what about:

    (1 2 3)(4 5)(6 7)(8 9)....(2n 2n+1).....

    and:

    (1 2)(3 4)(5 6)....(2n-1 2n)....

    can these be conjugate? why, or why not?
    Thanks from xixi
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