What is the inverse cycle of permutation? Given cyclic permutations, for example,
$σ = (123)$, $σ_{2} = (45)$,
what are the inverse cycles $σ^{-1}$, $σ_2^{-1}$?
Regards.

Every permutation n>1 can be expressed as a product of  2-cycles.
And every 2-cycle (transposition) is inverse of itself.
Therefore the inverse of a permutations is 
Just reverse products of its 2-cycles
(ab)^-1 = b^-1 a^-1
