|
gptkbp:instanceOf
|
gptkb:group_of_people
modular group
|
|
gptkbp:actsDiscretelyOn
|
upper half-plane
|
|
gptkbp:actsOn
|
upper half-plane
|
|
gptkbp:centralTo
|
gptkb:SL(2,ℤ)
|
|
gptkbp:definedIn
|
integers
|
|
gptkbp:finitelyGenerated
|
true
|
|
gptkbp:finitelyPresented
|
true
|
|
gptkbp:fullName
|
gptkb:Projective_Special_Linear_Group_of_2x2_integer_matrices_modulo_center
|
|
gptkbp:fundamentalDomain
|
modular region in upper half-plane
|
|
gptkbp:generation
|
S and T
|
|
gptkbp:hasInfiniteOrderElements
|
true
|
|
gptkbp:hasQuotients
|
gptkb:finite_simple_groups_PSL(2,p)
|
|
gptkbp:hasSubgroup
|
gptkb:Bianchi_groups
gptkb:Hecke_groups
gptkb:PSL(2,ℝ)
gptkb:principal_congruence_subgroups
congruence subgroups
|
|
gptkbp:hasTorsionElements
|
true
|
|
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
|
SL(2,ℤ) is 2
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isomorphicTo
|
free product of cyclic groups of order 2 and 3
|
|
gptkbp:isQuotientOf
|
gptkb:SL(2,ℤ)
gptkb:SL(2,ℤ)_by_{±I}
|
|
gptkbp:loveInterest
|
(ST)^3 = 1
S^2 = 1
T has infinite order
|
|
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
modular group action
|
|
gptkbp:usedIn
|
gptkb:modular_curves
gptkb:string_theory
gptkb:monstrous_moonshine
automorphic forms
modular symbols
modular function theory
|
|
gptkbp:bfsParent
|
gptkb:modular_group
|
|
gptkbp:bfsLayer
|
5
|