Let \(G\) be a group . A subgroup \(K\subseteq G\) is called normal if and only if \(g^{-1}Kg=K\) for every \(g\in G\).
Remarks
- If \(G\) is abelian, every subgroup is normal.
- The kernel of a homomorphism is normal.
Let \(G\) be a group . A subgroup \(K\subseteq G\) is called normal if and only if \(g^{-1}Kg=K\) for every \(g\in G\).