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. See also 
Diagonalizable group

References
. Group theory