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gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:modular_group
gptkb:discrete_group
|
|
gptkbp:acts_by
|
fractional linear transformations
|
|
gptkbp:actsOn
|
upper half-plane
|
|
gptkbp:centralTo
|
trivial
|
|
gptkbp:definedIn
|
PSL(2, Z) = SL(2, Z) / {±I}
|
|
gptkbp:generation
|
S
T
|
|
gptkbp:has_fundamental_domain
|
{z in H : |z| ≥ 1, -1/2 ≤ Re(z) ≤ 1/2}
|
|
gptkbp:hasProperty
|
non-abelian
finitely presented
free product of cyclic groups of order 2 and 3
|
|
gptkbp:hasSubgroup
|
gptkb:PSL(2,_R)
|
|
gptkbp:importantFor
|
complex analysis
modular forms
number theory
elliptic curves
|
|
gptkbp:loveInterest
|
(ST)^3 = 1
S^2 = 1
|
|
gptkbp:notable_quotient
|
gptkb:PSL(2,_Z/NZ)
|
|
gptkbp:notablePlace
|
S
T
|
|
gptkbp:notation
|
gptkb:modular_group
gptkb:PSL(2,_Z)
Γ
|
|
gptkbp:order
|
infinite
|
|
gptkbp:presentedBy
|
⟨S, T | S^2 = 1, (ST)^3 = 1⟩
|
|
gptkbp:quotient_space
|
gptkb:modular_group
|
|
gptkbp:relatedTo
|
modular arithmetic
modular functions
modular group action
modular group congruence subgroups
modular symbols
|
|
gptkbp:S_matrix
|
[[0, -1], [1, 0]]
|
|
gptkbp:studiedBy
|
gptkb:Felix_Klein
gptkb:Henri_Poincaré
gptkb:Richard_Dedekind
|
|
gptkbp:T_matrix
|
[[1, 1], [0, 1]]
|
|
gptkbp:used_in
|
gptkb:modular_curves
gptkb:string_theory
gptkb:monstrous_moonshine
automorphic forms
modular functions
modular forms theory
modular group tessellation
|
|
gptkbp:bfsParent
|
gptkb:Maass_forms
|
|
gptkbp:bfsLayer
|
7
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
modular group PSL(2, Z)
|