Normal Subgroup

A Subgroup H G 𝐻 𝐺 H\subseteq G is normal if it is invariant under Conjugation, EG: for all h H 𝐻 h\in H and g G 𝑔 𝐺 g\in G , g h g 1 H 𝑔 superscript 𝑔 1 𝐻 ghg^{-1}\in H .

Properties