Brauer third main theorem
= Brauer third main theorem
{c}
If a <block of a group algebra> $b$ of $kH$ has <defect group of a block> $D$ and $DC_G(D)\le H\le G$, then its <block induction> $b^G$ is the <principal block> if and only if $b$ is the <principal block>. Equivalently, the <Brauer morphism> of the principal block idempotent at any <p-subgroup> $Q$ is the principal block idempotent of $kC_G(Q)$.