infinite cycles in Sym(N)

**xixi** · February 26th 2013, 08:10 AM

I need an example of two infinite cycles in Sym(N) which are not conjugate.(N is the set of natural numbers)

**jakncoke** · February 26th 2013, 08:37 AM

I'm also interested in how you classify conjugancy classes on infinite cycles.

**xixi** · February 26th 2013, 11:25 PM

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).

**Deveno** · February 27th 2013, 03:14 AM

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?

Thread: infinite cycles in Sym(N)