Diagonal subgroup
In the mathematical discipline of group theory, for a given group the diagonal subgroup of the n-fold direct product is the subgroup
This subgroup is isomorphic to
Properties and applications
- If acts on a set the n-fold diagonal subgroup has a natural action on the Cartesian product induced by the action of on defined by
- If acts -transitively on then the -fold diagonal subgroup acts transitively on More generally, for an integer if acts -transitively on acts -transitively on
- Burnside's lemma can be proved using the action of the twofold diagonal subgroup.