Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
lattices in Euclidean space
|
| gptkbp:concerns |
gptkb:Euclidean_space
gptkb:crystallographic_groups discrete groups |
| gptkbp:field |
gptkb:geometry
crystallography |
| gptkbp:firstTheoremStates |
A crystallographic group in n-dimensional Euclidean space has a free abelian subgroup of rank n of finite index.
|
| https://www.w3.org/2000/01/rdf-schema#label |
Bieberbach theorem
|
| gptkbp:influenced |
classification of space groups
|
| gptkbp:namedAfter |
gptkb:Ludwig_Bieberbach
|
| gptkbp:numberOfTheorems |
three
|
| gptkbp:relatedTo |
flat manifold
space group |
| gptkbp:secondTheoremStates |
Any two crystallographic groups with isomorphic translation subgroups are affinely equivalent.
|
| gptkbp:thirdTheoremStates |
In each dimension n, there are only finitely many crystallographic groups up to affine equivalence.
|
| gptkbp:yearProposed |
1911
|
| gptkbp:bfsParent |
gptkb:Ludwig_Bieberbach
|
| gptkbp:bfsLayer |
5
|