Statements (31)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
modular group discrete group |
| gptkbp:actsDiscretelyOn |
gptkb:hyperbolic_plane
|
| gptkbp:actsOn |
upper half-plane
|
| gptkbp:centralTo |
trivial
|
| gptkbp:containsElement |
fractional linear transformation
|
| gptkbp:definedIn |
PSL(2,ℤ) = SL(2,ℤ)/{±I}
|
| gptkbp:generation |
S: z ↦ -1/z
T: z ↦ z+1 |
| gptkbp:hasApplication |
gptkb:algebraic_geometry
gptkb:topology complex analysis number theory theory of modular forms |
| gptkbp:hasSubgroup |
gptkb:principal_congruence_subgroup
gptkb:Hecke_group |
| https://www.w3.org/2000/01/rdf-schema#label |
modular group PSL(2,ℤ)
|
| gptkbp:indexedIn |
1 in itself
|
| gptkbp:isomorphicTo |
free product of C2 and C3
|
| gptkbp:isQuotientOf |
gptkb:SL(2,ℤ)
|
| gptkbp:notation |
gptkb:PSL(2,ℤ)
Γ |
| gptkbp:order |
infinite
|
| gptkbp:presentedBy |
⟨S,T | S^2 = (ST)^3 = 1⟩
|
| gptkbp:relatedTo |
modular forms
modular group modular equation modular function |
| gptkbp:bfsParent |
gptkb:SL(2,ℤ)
|
| gptkbp:bfsLayer |
6
|