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(Moderator's note: thread moved from "Set Theory, Logic, Probability, Statistics")

the question is

if n is odd then there are exactly two conjugacy classes of n cycles in An each of which contains (n-1)!/2 elements.

also there is a hint says let An act on itself

i know the fact that since An acts on itself, x doesnt commute with any odd permutation. So it splits into two Ccl An (x) and CCl An (12)x(12).

But i cant figure it out how to calculate either the number of stabilizers or the number of orbits

the question is

if n is odd then there are exactly two conjugacy classes of n cycles in An each of which contains (n-1)!/2 elements.

also there is a hint says let An act on itself

i know the fact that since An acts on itself, x doesnt commute with any odd permutation. So it splits into two Ccl An (x) and CCl An (12)x(12).

But i cant figure it out how to calculate either the number of stabilizers or the number of orbits

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