Subgroup

Sous-groupe (Fr); Untergruppe (Ge); Subgrupo (Sp); Sottogruppo (It); 部分群 (Ja).

Let G be a group and H a non-empty subset of G. Then H is called a subgroup of H if the elements of H obey the group postulates.

The subgroup H is called a proper subgroup of G if there are elements of G not contained in H.

A subgroup H of G is called a maximal subgroup of G if there is no proper subgroup M of G such that H is a proper subgroup of M.

See also

• Coset
• Normal subgroup
• Section 8.3.3 in the International Tables for Crystallography, Volume A