Editing Normal subgroup (section)

=== Lattice of normal subgroups ===
Given two normal subgroups, <math>N</math> and <math>M</math>, of <math>G</math>, their intersection <math>N\cap M</math> and their [[Product of subgroups|product]] <math>N M = \{n m : n \in N\; \text{ and }\; m \in M \}</math> are also normal subgroups of <math>G</math>. 

The normal subgroups of <math>G</math> form a [[Lattice (order)|lattice]] under [[subset inclusion]] with [[least element]], <math>\{ e \}</math>, and [[greatest element]], <math>G</math>. The [[Meet (lattice theory)|meet]] of two normal subgroups, <math>N</math> and <math>M</math>, in this lattice is their intersection and the [[Join (lattice theory)|join]] is their product.

The lattice is [[Complete lattice|complete]] and [[Modular lattice|modular]].{{sfn|Hungerford|2003|p=46}}