Statements (50)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
|
| gptkbp:actsOn |
upper half-plane
fractional linear transformations |
| gptkbp:alsoKnownAs |
modular group
|
| gptkbp:centralTo |
trivial
|
| gptkbp:definedIn |
integers
|
| gptkbp:fullName |
gptkb:Projective_Special_Linear_Group_of_2x2_matrices_over_the_integers
|
| gptkbp:generation |
S
T |
| gptkbp:hasCayleyGraph |
infinite tree
|
| gptkbp:hasCongruenceSubgroups |
yes
|
| gptkbp:hasProperty |
modular group
non-abelian orthogonal group finitely generated residually finite virtually free group not finite Hopfian Kazhdan's property (T) does not hold Tits alternative holds co-Hopfian congruence subgroup property does not hold discrete subgroup of PSL(2,R) lattice in PSL(2,R) property (FAb) does not hold property FA does not hold word-hyperbolic |
| gptkbp:hasSubgroup |
gptkb:PSL(2,R)
|
| https://www.w3.org/2000/01/rdf-schema#label |
PSL(2,Z)
|
| gptkbp:importantFor |
gptkb:hyperbolic_geometry
complex analysis modular forms number theory |
| gptkbp:indexIn |
PSL(2,R) is infinite
|
| gptkbp:isomorphicTo |
C2 * C3
free product of C2 and C3 |
| gptkbp:isQuotientOf |
gptkb:SL(2,Z)
|
| gptkbp:order |
infinite
|
| gptkbp:presentedBy |
generated by S and T with relations S^2 = (ST)^3 = 1
|
| gptkbp:relatedTo |
gptkb:monodromy_group
gptkb:triangle_group_(2,3,∞) gptkb:Farey_tessellation modular forms modular functions modular group continued fractions modular group action |
| gptkbp:bfsParent |
gptkb:mapping_class_group_of_the_torus
|
| gptkbp:bfsLayer |
6
|