Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
orthogonal group |
| gptkbp:actsOn |
Z^n
|
| gptkbp:application |
gptkb:geometry_of_numbers
gptkb:algebraic_K-theory crystallography number theory lattice theory |
| gptkbp:centralTo |
{I, -I} for even n
{I} for odd n |
| gptkbp:containsElement |
invertible n x n matrices with integer entries
|
| gptkbp:determinantCondition |
determinant is ±1
|
| gptkbp:field |
Z
|
| gptkbp:finitelyGenerated |
true
|
| gptkbp:fullName |
gptkb:general_linear_group_of_degree_n_over_the_integers
|
| gptkbp:hasSubgroup |
gptkb:GL(n,Q)
|
| https://www.w3.org/2000/01/rdf-schema#label |
GL(n,Z)
|
| gptkbp:identityElement |
identity matrix
matrix inverse |
| gptkbp:importantSubgroup |
gptkb:SL(n,Z)
|
| gptkbp:notation |
gptkb:GL_n(Z)
|
| gptkbp:order |
infinite
|
| gptkbp:relatedGroup |
matrix multiplication
|
| gptkbp:relatedTo |
gptkb:modular_group_(for_n=2)
|
| gptkbp:bfsParent |
gptkb:torus_group
gptkb:modular_group |
| gptkbp:bfsLayer |
5
|