Let m>1 be an odd natural number, x a m-cycle in Am, the alternating group in m letters, C the conjugacy class of x in Am.

Questiom: How can I describe the elements in the set { j | x^j in C} in terms of m?

For instance, if C' is the conjugacy class of x in Sm, the symmetric group in m letters, then { j | x^j in C} = { j | (j,m)=1 }, where (j,m) = Greatest common divisor of j and m. But in Am, C' splits in two conjugacy classes of Am of the same size: C and the conjugacy class of (1 2)x(1 2) in Am.

Thank you in advance. Fernando.