Symmetric groups are rational
This article describes a basic fact about permutations, or about the symmetric group or alternating group.
View a complete list of basic facts about permutations
- Finitary symmetric group on infinite set is rational
- Finitary alternating group on infinite set is rational
- Symmetric groups are ambivalent
- Symmetric groups are strongly ambivalent
- Take any permutation . Express it using its cycle decomposition.
- Show that any other permutation generating the same cyclic group has the same cycle type as .
- Use the fact that any two permutations with the same cycle type, are conjugate inside the symmetric group.