defect

《Cohomologie Locale Des Faisceaux Coherents (Sga 2): Seminaire De Geometrie Algebrique Du Bois Marie 1962 (Documents Mathematiques)》 · 印刷第 267—268 页 Section 12.3「The Defect of a Block: Module Theoretic Methods」，对角嵌入约定、Corollary 12.3.2 完整陈述及随后亏群和亏数的定义；此处取整数语境，不将亏群本身录为别名

It will be important to consider the diagonal embedding of $\delta:G\to G\times G$ specified by $\delta(g)=(g,g)$. […] Corollary 12.3.2. Let $R$ be a discrete valuation ring with residue field of characteristic $p$ (or a field of characteristic $p$). Let $G$ be a finite group and let $e$ be a block of $RG$. Then, regarded as a $R[G\times G]$-module, the summand $eRG$ has a vertex of the form $\delta(D)$ where $D$ is a $p$-subgroup of $G$. Such a subgroup $D$ is uniquely defined to within conjugacy in $G$. […] Let $R$ be a discrete valuation ring with residue field of characteristic $p$ and let $e\in Z(RG)$ be a $p$-block of $G$. We define a subgroup $D$ of $G$ to be a defect group of the block $e$ if $\delta(D)$ is a vertex of $eRG$ as an $R[G\times G]$-module. According to Corollary 12.3.2, $D$ is defined up to conjugacy in $G$ and is a $p$-group. If $|D|=p^d$, we say that $d$ is the defect of $e$, but often we abuse this terminology and say simply that the defect of the block is $D$.