Editing Permutation (section)

===Conjugating permutations===
In general, composing permutations written in cycle notation follows no easily described pattern – the cycles of the composition can be different from those being composed. However the cycle type is preserved in the special case of [[conjugacy class|conjugating]] a permutation <math>\sigma</math> by another permutation <math>\pi</math>, which means forming the product <math>\pi\sigma\pi^{-1}</math>. Here, <math>\pi\sigma\pi^{-1}</math> is the ''conjugate'' of <math>\sigma</math> by <math>\pi</math> and its cycle notation can be obtained by taking the cycle notation for <math>\sigma</math> and applying <math>\pi</math> to all the entries in it.{{sfn|Humphreys|1996|p=84}} It follows that two permutations are conjugate exactly when they have the same cycle type.