|
gptkbp:instanceOf
|
gptkb:group_of_people
|
|
gptkbp:actsOn
|
upper half-plane
|
|
gptkbp:centralTo
|
trivial
|
|
gptkbp:fullName
|
gptkb:Projective_Special_Linear_Group_of_2x2_matrices_over_the_integers
|
|
gptkbp:generation
|
images of matrices S and T
|
|
gptkbp:hasCayleyGraph
|
infinite tree
|
|
gptkbp:hasElementOrder
|
2
3
|
|
gptkbp:hasSubgroup
|
gptkb:PSL_2(R)
congruence subgroups
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
PSL 2(Z)
|
|
gptkbp:isAlgebraicGroup
|
true
|
|
gptkbp:isDiscreteSubgroupOf
|
gptkb:PSL_2(R)
|
|
gptkbp:isFinitelyGenerated
|
true
|
|
gptkbp:isMatrixGroup
|
true
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isomorphicTo
|
free product of cyclic groups of order 2 and 3
|
|
gptkbp:isQuotientOf
|
gptkb:SL_2(Z)
|
|
gptkbp:isResiduallyFinite
|
true
|
|
gptkbp:isTorsionFree
|
false
|
|
gptkbp:isUniversal
|
true
|
|
gptkbp:notation
|
gptkb:PSL_2(Z)
|
|
gptkbp:order
|
infinite
|
|
gptkbp:presentedBy
|
<a,b | a^2 = b^3 = 1>
|
|
gptkbp:relatedTo
|
modular group
|
|
gptkbp:usedIn
|
gptkb:hyperbolic_geometry
gptkb:Riemann_surfaces
gptkb:monodromy_groups
modular forms
number theory
|
|
gptkbp:bfsParent
|
gptkb:SL_2(Z)
gptkb:PSL(2,_Z)
|
|
gptkbp:bfsLayer
|
7
|