Normal subgroup

Sousgroupe normal (Fr); Sottogruppo normale (It).

Definition

A subgroup H of a group G is normal if gH = Hg for any g ∈G. Equivalently, H ⊂ G is normal if and only if gHg^-1 = H for any g ∈G, i.e., if and only if each conjugacy class of G is either entirely inside H or entirely outside H.