Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
orthogonal group |
| gptkbp:actsOn |
ℤ^2
|
| gptkbp:application |
crystallography
modular forms number theory lattice theory |
| gptkbp:centralTo |
{±I}
|
| gptkbp:containsElement |
2×2 invertible matrices with integer entries
|
| gptkbp:determinant |
±1
|
| gptkbp:fullName |
general linear group of 2×2 invertible matrices over the integers
|
| gptkbp:hasSubgroup |
gptkb:SL(2,ℤ)
GL(2,ℚ) |
| https://www.w3.org/2000/01/rdf-schema#label |
GL(2,ℤ)
|
| gptkbp:identityElement |
matrix inverse
2×2 identity matrix |
| gptkbp:isQuotientOf |
GL(2,ℤ)/SL(2,ℤ) ≅ C2
|
| gptkbp:notation |
GL_2(ℤ)
|
| gptkbp:operator |
matrix multiplication
|
| gptkbp:order |
infinite
|
| gptkbp:relatedTo |
modular group
automorphism group of free abelian group of rank 2 |
| gptkbp:bfsParent |
gptkb:SL(2,ℤ)
|
| gptkbp:bfsLayer |
6
|