Statements (31)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
modular group discrete group |
| gptkbp:actsOn |
upper half-plane
|
| gptkbp:centralTo |
{±I}
|
| gptkbp:containsElement |
2x2 integer matrices with determinant 1
|
| gptkbp:generation |
S = [[0,-1],[1,0]]
T = [[1,1],[0,1]] |
| gptkbp:hasIndex2Subgroup |
Γ(2)
|
| gptkbp:hasSubgroup |
gptkb:SL(2,ℝ)
|
| https://www.w3.org/2000/01/rdf-schema#label |
modular group SL(2,ℤ)
|
| gptkbp:isNonAbelian |
true
|
| gptkbp:isQuotientOf |
gptkb:PSL(2,ℤ)
|
| gptkbp:loveInterest |
(ST)^3 = I
S^4 = I |
| gptkbp:notation |
gptkb:SL(2,ℤ)
|
| gptkbp:order |
infinite
|
| gptkbp:presentedBy |
⟨S,T | S^4 = I, (ST)^3 = I⟩
|
| gptkbp:relatedTo |
modular group
modular polynomial modular group action modular symmetry |
| gptkbp:usedIn |
gptkb:hyperbolic_geometry
complex analysis modular forms number theory elliptic curves modular functions |
| gptkbp:bfsParent |
gptkb:modular_discriminant
gptkb:Ramanujan_Delta_function |
| gptkbp:bfsLayer |
7
|