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 are conjugate in iff they have the same number of cycles of each type (including 1-cycles).
(1 2 3)(4 5)(6 7)(8 9)....(2n 2n+1).....
(1 2)(3 4)(5 6)....(2n-1 2n)....
can these be conjugate? why, or why not?
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