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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- Feb 26th 2013, 08:10 AMxixiinfinite 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)

- Feb 26th 2013, 08:37 AMjakncokeRe: infinite cycles in Sym(N)
I'm also interested in how you classify conjugancy classes on infinite cycles.

- Feb 26th 2013, 11:25 PMxixiRe: infinite cycles in Sym(N)
Two permutations $\displaystyle x,y \in Sym(\Omega)$ are conjugate in $\displaystyle Sym(\Omega)$ iff they have the same number of cycles of each type (including 1-cycles).

- Feb 27th 2013, 03:14 AMDevenoRe: 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?