|
gptkbp:instanceOf
|
gptkb:group_of_people
|
|
gptkbp:actsOn
|
upper half-plane
|
|
gptkbp:application
|
gptkb:hyperbolic_geometry
gptkb:monodromy_groups
modular forms
number theory
automorphic forms
Galois representations
|
|
gptkbp:centralTo
|
{I, -I}
|
|
gptkbp:containsElement
|
matrices with integer entries and determinant 1
|
|
gptkbp:defines
|
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:hasCongruenceSubgroupProperty
|
false
|
|
gptkbp:hasElementOrder
|
2
4
6
|
|
gptkbp:hasIndexIn
|
infinite in SL_2(R)
|
|
gptkbp:hasKazhdanPropertyT
|
false
|
|
gptkbp:hasPropertyT
|
false
|
|
gptkbp:hasSubgroup
|
gptkb:SL_2(R)
congruence subgroups
|
|
gptkbp:hasTorsionElements
|
true
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SL 2(Z)
|
|
gptkbp:identityElement
|
2x2 identity matrix
|
|
gptkbp:isAlgebraicGroup
|
true
|
|
gptkbp:isCocompact
|
false
|
|
gptkbp:isCofinitelyGenerated
|
true
|
|
gptkbp:isCountable
|
true
|
|
gptkbp:isDenseIn
|
SL_2(R) (in Zariski topology)
|
|
gptkbp:isDiscreteIn
|
gptkb:SL_2(R)_(in_analytic_topology)
|
|
gptkbp:isDiscreteSubgroupOf
|
gptkb:SL_2(R)
|
|
gptkbp:isFinitelyGenerated
|
true
|
|
gptkbp:isHopfian
|
true
|
|
gptkbp:isLatticeIn
|
gptkb:SL_2(R)
|
|
gptkbp:isMatrixGroup
|
true
|
|
gptkbp:isModularGroup
|
false
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isomorphicTo
|
free product of C_4 and C_6 modulo C_2
|
|
gptkbp:isPerfect
|
false
|
|
gptkbp:isQuotientOf
|
gptkb:PSL_2(Z)
|
|
gptkbp:isResiduallyFinite
|
true
|
|
gptkbp:isTorsionFree
|
false
|
|
gptkbp:matrixSize
|
2x2
|
|
gptkbp:notation
|
gptkb:SL_2(Z)
|
|
gptkbp:operator
|
matrix multiplication
|
|
gptkbp:order
|
infinite
|
|
gptkbp:presentedBy
|
<S,T | S^4=I, (ST)^3=I>
|
|
gptkbp:relatedTo
|
gptkb:modular_group_PSL_2(Z)
|
|
gptkbp:bfsParent
|
gptkb:Gamma_1(N)
|
|
gptkbp:bfsLayer
|
6
|