Normal subgroup

From Online Dictionary of Crystallography

Sousgroupe normal (Fr); Sottogruppo normale (It); 正規部分群 (Ja)

Definition

A subgroup H of a group G is normal (H G) 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.