Brauer extended first main theorem
= Brauer extended first main theorem
{c}
Over a <splitting field for finite group representations>, <blocks of a group algebra> with <defect group of a block> $D$ correspond to $N_G(D)$-orbits of blocks $b_D$ of $k(DC_G(D))$ with defect $D$ whose stabilizer quotient $N_G(D,b_D)/(DC_G(D))$ has order coprime to $p$. Equivalently one uses the defect-zero block of $k(DC_G(D)/D)$. This quotient is the <inertial quotient of a block>.