Defect group of a block
= Defect group of a block
A defect group of a block idempotent $e$ is a maximal p-subgroup $D$ for which the Brauer image $\operatorname{Br}_D(e)$ is nonzero. Equivalently, the vertices of the block algebra as an $R[G\times G]$-module are the diagonal subgroups $\Delta D$ for the defect groups $D$. All defect groups of a block are conjugate.