|
gptkbp:instanceOf
|
gptkb:group_of_people
modular group
|
|
gptkbp:action
|
fractional linear transformations
|
|
gptkbp:actsOn
|
upper half-plane
|
|
gptkbp:category
|
gptkb:group_of_people
modular group
orthogonal group
non-abelian group
infinite group
discrete group
|
|
gptkbp:centerOfSL(2,_Z)
|
{±I}
|
|
gptkbp:definedIn
|
SL(2, Z) modulo its center
|
|
gptkbp:fullName
|
gptkb:Projective_Special_Linear_Group_of_2x2_matrices_over_the_integers
|
|
gptkbp:generation
|
S and T
|
|
gptkbp:hasSubgroup
|
gptkb:principal_congruence_subgroup
gptkb:PSL(2,_R)
gptkb:Hecke_groups
congruence subgroups
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
PSL(2, Z)
|
|
gptkbp:importantFor
|
gptkb:hyperbolic_geometry
complex analysis
modular forms
number theory
|
|
gptkbp:indexInSL(2,_Z)
|
2
|
|
gptkbp:isomorphicTo
|
free product of C2 and C3
|
|
gptkbp:isQuotientOf
|
gptkb:SL(2,_Z)
|
|
gptkbp:loveInterest
|
(ST)^3 = 1
S^2 = 1
|
|
gptkbp:notation
|
gptkb:PSL_2(Z)
Γ
|
|
gptkbp:order
|
infinite
|
|
gptkbp:presentedBy
|
<S, T | S^2 = 1, (ST)^3 = 1>
|
|
gptkbp:relatedTo
|
gptkb:monodromy_group
gptkb:triangle_group_(2,3,∞)
gptkb:Farey_tessellation
modular forms
modular group
continued fractions
|
|
gptkbp:bfsParent
|
gptkb:Modular_group
gptkb:SL(2,_Z)
gptkb:modular_group_PSL(2,_Z)
|
|
gptkbp:bfsLayer
|
6
|