|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:modular_group
gptkb:discrete_group
|
|
gptkbp:actsOn
|
upper half-plane
fractional linear transformations
|
|
gptkbp:alternativeName
|
gptkb:modular_group
gptkb:PSL(2,_Z)
projective special linear group over integers
|
|
gptkbp:centralTo
|
trivial
|
|
gptkbp:definedIn
|
PSL_2(Z) = SL_2(Z) / {±I}
|
|
gptkbp:generation
|
S = [[0,-1],[1,0]]
T = [[1,1],[0,1]]
|
|
gptkbp:hasProperty
|
gptkb:orthogonal_group
residually finite
non-solvable
non-amenable
|
|
gptkbp:hasSubgroup
|
congruence subgroups
|
|
gptkbp:indexedIn
|
1 in itself
6 in SL_2(Z)
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isomorphicTo
|
free product of C2 and C3
|
|
gptkbp:isQuotientOf
|
gptkb:SL_2(Z)
|
|
gptkbp:order
|
infinite
|
|
gptkbp:presentedBy
|
<S,T | S^2 = (ST)^3 = 1>
|
|
gptkbp:relatedTo
|
gptkb:monodromy_group
gptkb:triangle_group_(2,3,∞)
gptkb:Riemannian_manifold
gptkb:modular_group
gptkb:Farey_tessellation
gptkb:modular_function
modular forms
automorphic forms
elliptic curves
continued fractions
|
|
gptkbp:bfsParent
|
gptkb:SL_2(Z)
|
|
gptkbp:bfsLayer
|
8
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
modular group PSL 2(Z)
|