core

Last updated January 27, 2022

Idea

The normal core of a subgroup $H\subset G$ is the largest normal subgroup of $G$ contained in $H$.

Definition

Let $G$ be a group and $H$ a subgroup.

• The normal core of $H$ is the largest normal subgroup of $G$ contained in $H$. Explicitly, $$\text{Core}G(H)=\bigcap{g\in G}gHg^{-1}.$$