= Block induction
{title2=$b^G$}
Let $b$ be a <block of a group algebra> of $kH$ with <defect group of a block> $D$, where $DC_G(D)\le H\le G$. Apply <Brauer first main theorem> inside $H$ to obtain its correspondent in $N_H(D)$. Composing that correspondent's <central character of a block> with the <Brauer morphism> from $Z(kG)$ selects a unique <block of a group algebra> $b^G$. It is the unique <block of a group algebra> whose restriction to $H\times H$ contains the block bimodule $b$ as a <direct summand>. Its <defect group of a block> can be larger than $D$ when $H$ does not contain $N_G(D)$.
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