• 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 :(x_1, \dots, x_n) \cdot (g, \dots, g) = (x_1 \!\cdot g, \dots, x_n \!\cdot g). • 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 ==