|
gptkbp:instanceOf
|
gptkb:group_of_people
discrete group
|
|
gptkbp:actsOn
|
upper half-plane
|
|
gptkbp:automorphismGroup
|
gptkb:GL(2,ℤ)
trivial
|
|
gptkbp:centralTo
|
{I, -I}
|
|
gptkbp:containsElement
|
2x2 matrices with integer entries and determinant 1
|
|
gptkbp:definedIn
|
the group of 2x2 integer matrices with determinant 1
|
|
gptkbp:fullName
|
gptkb:special_linear_group_of_2x2_integer_matrices
|
|
gptkbp:generation
|
S = [[0,-1],[1,0]]
T = [[1,1],[0,1]]
|
|
gptkbp:hasProperty
|
modular group
orthogonal group
finitely generated
residually finite
non-nilpotent
non-solvable
not finitely presented
perfect group
|
|
gptkbp:hasSubgroup
|
gptkb:SL(2,ℝ)
gptkb:Γ(n)_(principal_congruence_subgroup_of_level_n)
congruence subgroups
Γ_0(n)
Γ_1(n)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SL(2,ℤ)
|
|
gptkbp:importantFor
|
gptkb:algebraic_geometry
gptkb:topology
modular forms
number theory
theory of Riemann surfaces
|
|
gptkbp:indexOfCenter
|
2
|
|
gptkbp:isFinite
|
true
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isomorphicTo
|
universal central extension of PSL(2,ℤ)
|
|
gptkbp:isQuotientOf
|
gptkb:PSL(2,ℤ)
|
|
gptkbp:notation
|
gptkb:SL(2,Z)
gptkb:SL_2(ℤ)
|
|
gptkbp:operator
|
matrix multiplication
|
|
gptkbp:presentedBy
|
⟨S,T | S^4=I, (ST)^3=I⟩
|
|
gptkbp:relatedTo
|
gptkb:modular_curves
gptkb:monodromy_groups
gptkb:Farey_tessellation
gptkb:mapping_class_group_of_the_torus
gptkb:modular_group_PSL(2,ℤ)
automorphic forms
modular group
continued fractions
|
|
gptkbp:bfsParent
|
gptkb:modular_group
|
|
gptkbp:bfsLayer
|
5
|