Group algebra of a p-group in characteristic p is local
= Group algebra of a p-group in characteristic p is local
{title2=$kG$ for a $p$-group $G$}
If $G$ is a finite $p$-group and $k$ has characteristic $p$, then the <augmentation ideal> is the <Jacobson radical> of $kG$ and $kG/J(kG)\cong k$. Thus $kG$ is a <local ring>, has only the trivial simple module, and its regular module is indecomposable.