# normal subgroup

A subgroup \(N\) of \(G\) is normal if and only if \(gng^-1 \in N\) for every \(n\) in \(N\) and \(g\) in \(G\)

## 1. properties

- for all \(g\in G\) the left coset
- this mostly comes up in the context of quotient groups
- see intuition (not very good)