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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I'm also interested in how you classify conjugancy classes on infinite cycles.
Last edited by jakncoke; Feb 26th 2013 at 09:43 AM.
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).
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?
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