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gptkbp:instanceOf
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Mathematical group
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gptkbp:action
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gptkb:Möbius_transformations
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gptkbp:actsOn
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gptkb:Upper_half-plane
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gptkbp:alsoKnownAs
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gptkb:PSL(2,_Z)
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gptkbp:centralTo
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Trivial
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gptkbp:containsElement
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Equivalence classes of 2x2 integer matrices with determinant 1
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gptkbp:defines
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The group of 2x2 matrices with integer entries and determinant 1, modulo its center.
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gptkbp:field
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gptkb:Mathematics
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gptkbp:generation
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S and T
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gptkbp:hasApplication
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gptkb:Algebraic_geometry
Monodromy of differential equations
Theory of modular forms
Theory of tessellations
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gptkbp:hasCayleyGraph
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Infinite tree
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gptkbp:hasFundamentalDomain
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Standard fundamental domain in upper half-plane
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gptkbp:hasQuotientSpace
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gptkb:Modular_curve
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gptkbp:hasSubfield
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gptkb:Number_theory
gptkb:Group_theory
Complex analysis
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gptkbp:hasSubgroup
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gptkb:Congruence_subgroup
gptkb:Gamma_0(N)
gptkb:Gamma_1(N)
gptkb:Principal_congruence_subgroup
Gamma(N)
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https://www.w3.org/2000/01/rdf-schema#label
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Modular group
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gptkbp:importantFor
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gptkb:Riemann_surfaces
gptkb:Automorphic_forms
gptkb:Modular_forms
Elliptic curves
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gptkbp:isAlgebraicGroup
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True
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gptkbp:isDiscrete
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True
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gptkbp:isFinitelyGenerated
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True
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gptkbp:isMatrixGroup
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True
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gptkbp:isNon-abelian
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True
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gptkbp:isQuotientOf
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gptkb:SL(2,_Z)/{±I}
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gptkbp:loveInterest
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(ST)^3 = 1
S^2 = 1
T has infinite order
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gptkbp:notation
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gptkb:PSL(2,_Z)
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gptkbp:order
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Infinite
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gptkbp:presentedBy
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<S, T | S^2 = 1, (ST)^3 = 1>
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gptkbp:relatedTo
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gptkb:Hecke_group
gptkb:Bianchi_group
gptkb:Triangle_group
modular group
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gptkbp:studiedBy
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gptkb:Felix_Klein
gptkb:Henri_Poincaré
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gptkbp:bfsParent
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gptkb:Triangle_Group
gptkb:Modular_form
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gptkbp:bfsLayer
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5
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