Inflated quotient projectives have trivial source
= Inflated quotient projectives have trivial source
If $D$ is a normal <p-subgroup> of $N$, any indecomposable <projective module> of $k(N/D)$, inflated to $N$, is a summand of $k[N/D]=\operatorname{Ind}_D^Nk$. It has trivial source and vertex $D$. Its <Brauer quotient of a module> at $D$ is the entire module, since $D$ acts trivially and all proper-subgroup <relative traces> multiply by an index divisible by $p$. This prevents its vertex from being smaller than $D$.