# Subgroup

### From Online Dictionary of Crystallography

##### Revision as of 17:16, 25 April 2007 by MassimoNespolo (talk | contribs)

Revision as of 17:16, 25 April 2007 by MassimoNespolo (talk | contribs)

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*