Statements (37)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
modular group discrete group |
| gptkbp:actsOn |
upper half-plane
fractional linear transformations |
| gptkbp:alternativeName |
gptkb:PSL(2,_Z)
modular group projective special linear group over integers |
| gptkbp:centralTo |
trivial
|
| gptkbp:definedIn |
PSL_2(Z) = SL_2(Z) / {±I}
|
| gptkbp:generation |
S = [[0,-1],[1,0]]
T = [[1,1],[0,1]] |
| gptkbp:hasProperty |
orthogonal group
residually finite non-solvable non-amenable |
| gptkbp:hasSubgroup |
congruence subgroups
|
| https://www.w3.org/2000/01/rdf-schema#label |
modular group PSL 2(Z)
|
| gptkbp:indexedIn |
1 in itself
6 in SL_2(Z) |
| gptkbp:isNonAbelian |
true
|
| gptkbp:isomorphicTo |
free product of C2 and C3
|
| gptkbp:isQuotientOf |
gptkb:SL_2(Z)
|
| gptkbp:order |
infinite
|
| gptkbp:presentedBy |
<S,T | S^2 = (ST)^3 = 1>
|
| gptkbp:relatedTo |
gptkb:monodromy_group
gptkb:triangle_group_(2,3,∞) gptkb:Riemannian_manifold gptkb:Farey_tessellation modular forms automorphic forms elliptic curves modular group continued fractions modular function |
| gptkbp:bfsParent |
gptkb:SL_2(Z)
|
| gptkbp:bfsLayer |
7
|