4.14 (1973)

Let $p$ be a prime number. What are necessary and sufficient conditions for a finite group $G$ in order that the group algebra of $G$ over a field of characteristic $p$ be indecomposable as a two-sided ideal? There exist some nontrivial examples, for instance, the group algebra of the Mathieu group $M_{24}$ is indecomposable when $p$ is 2.