Lecture Notes on Bayesian Estimation and Classification
《Lecture Notes on Bayesian Estimation and Classification》 · 第 16 页 · Section 1.3「Subgroups and Cosets」，小节「Normal Closure and Core」
Dual to the normal closure is $X_G$, the normal interior or core of $X$ in $G$; this is defined to be the join of all the normal subgroups of $G$ that are contained in $X$, with the convention that $X_G=1$ if there are no such subgroups. Again it is simple to prove that $H_G=\bigcap_{g\in G}g^{-1}Hg$ for $H$ a subgroup.