Maschke's averaging lemma for abelian groups
Suppose we have an action of on by automorphisms. Then, if is a direct factor of that is invariant under the -action, there exists a complement to in that is also invariant under the -action.
- Maschke's averaging lemma: Here, the Abelian group is the additive group of a field whose characteristic does not divide the order of the group. The condition on the characteristic of the field.