|
gptkbp:instanceOf
|
gptkb:group_of_people
|
|
gptkbp:actsOn
|
upper half-plane
|
|
gptkbp:centralTo
|
{I, -I}
|
|
gptkbp:compact
|
true
|
|
gptkbp:contains
|
-identity matrix
identity matrix
|
|
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:hasIndex2Subgroup
|
PSL_2(ℤ)
|
|
gptkbp:hasKazhdanPropertyT
|
false
|
|
gptkbp:hasPropertyT
|
false
|
|
gptkbp:hasSubgroup
|
gptkb:principal_congruence_subgroup
congruence subgroups
GL_2(ℤ)
|
|
gptkbp:hasTorsionElements
|
true
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SL 2(ℤ)
|
|
gptkbp:isAlgebraicGroup
|
true
|
|
gptkbp:isAmalgamatedProduct
|
C_4 *_{C_2} C_6
|
|
gptkbp:isArithmetic
|
true
|
|
gptkbp:isCountable
|
true
|
|
gptkbp:isDenseIn
|
SL_2(ℝ)
|
|
gptkbp:isDiscrete
|
true
|
|
gptkbp:isDiscreteSubgroupOf
|
SL_2(ℝ)
|
|
gptkbp:isFinitelyGenerated
|
true
|
|
gptkbp:isFuchsianGroup
|
true
|
|
gptkbp:isHopfian
|
true
|
|
gptkbp:isLatticeIn
|
SL_2(ℝ)
|
|
gptkbp:isLinearGroupOver
|
ℤ
|
|
gptkbp:isMatrixGroup
|
true
|
|
gptkbp:isModularGroup
|
true
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isNonNilpotent
|
true
|
|
gptkbp:isPerfect
|
false
|
|
gptkbp:isQuotientOf
|
PSL_2(ℤ)
|
|
gptkbp:isResiduallyFinite
|
true
|
|
gptkbp:isSimple
|
true
|
|
gptkbp:isSolvable
|
true
|
|
gptkbp:isTorsionFree
|
false
|
|
gptkbp:isUniversalCentralExtensionOf
|
PSL_2(ℤ)
|
|
gptkbp:isVirtuallyFree
|
true
|
|
gptkbp:notation
|
gptkb:SL_2(Z)
|
|
gptkbp:order
|
infinite
|
|
gptkbp:presentedBy
|
<S,T | S^4=I, (ST)^3=I>
|
|
gptkbp:relatedTo
|
gptkb:modular_curves
modular forms
modular group
|
|
gptkbp:bfsParent
|
gptkb:SL(2,ℤ)
|
|
gptkbp:bfsLayer
|
6
|