Maschke lemma

Statement

Let be a finite group and be a field. If then is a semisimple ring.

Proof

todo - Lecture 24

Examples

• For a field with characteristic 0, the is not a restriction. That means is semisimple for and , for any group .

• (Non-example:) , , then the ring is not semisimple, not in .

Importance

Given the conditions needed, i.e. the characteristic of the