# Difference between revisions of "Subgroup"

### From Online Dictionary of Crystallography

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==See also== | ==See also== | ||

− | *[[ Normal subgroup]] | + | * [[Coset]] |

+ | *[[Normal subgroup]] | ||

*Section 8.3.3 in the ''International Tables for Crystallography, Volume A'' | *Section 8.3.3 in the ''International Tables for Crystallography, Volume A'' | ||

[[Category:Fundamental crystallography]] | [[Category:Fundamental crystallography]] |

## Revision as of 17:16, 25 April 2007

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*