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gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:discrete_subgroup
gptkb:modular_group
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|
gptkbp:actsOn
|
ℤ^n
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|
gptkbp:centralTo
|
{I, -I} (for n even)
{I} (for n odd)
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|
gptkbp:definedIn
|
the group of n×n integer matrices with determinant 1
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|
gptkbp:fullName
|
gptkb:Special_Linear_Group_of_degree_n_over_the_integers
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|
gptkbp:generation
|
elementary matrices
|
|
gptkbp:hasCongruenceSubgroups
|
true
|
|
gptkbp:hasFiniteIndexSubgroups
|
true
|
|
gptkbp:hasKazhdanPropertyT
|
true (for n>2)
|
|
gptkbp:hasProperty
|
congruence subgroup property (for n>2)
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|
gptkbp:hasSubgroup
|
gptkb:principal_congruence_subgroup
congruence subgroups
GL(n,ℤ)
SL(n,ℝ)
|
|
gptkbp:isAlgebraicGroup
|
true
|
|
gptkbp:isCocompact
|
false
|
|
gptkbp:isCountable
|
true
|
|
gptkbp:isDenseIn
|
SL(n,ℝ) (in Zariski topology)
|
|
gptkbp:isDiscrete
|
true
|
|
gptkbp:isDiscreteIn
|
SL(n,ℝ)
|
|
gptkbp:isFinite
|
true
|
|
gptkbp:isFinitelyGenerated
|
true
|
|
gptkbp:isFinitelyPresented
|
true
|
|
gptkbp:isHopfian
|
true
|
|
gptkbp:isLatticeIn
|
SL(n,ℝ)
|
|
gptkbp:isLinearOver
|
ℝ
ℤ
|
|
gptkbp:isMatrixGroup
|
true
|
|
gptkbp:isNonAbelian
|
true (for n>1)
|
|
gptkbp:isPerfect
|
true (for n>2)
|
|
gptkbp:isQuotientOf
|
PSL(n,ℤ)
|
|
gptkbp:isResiduallyFinite
|
true
|
|
gptkbp:isSimple
|
false (for n>2)
false (for n=2)
|
|
gptkbp:isTorsionFree
|
false
|
|
gptkbp:isUnimodular
|
true
|
|
gptkbp:notation
|
gptkb:SL(n,Z)
SL_n(Z)
|
|
gptkbp:relatedTo
|
gptkb:modular_group_(for_n=2)
automorphism group of free abelian group of rank n
|
|
gptkbp:bfsParent
|
gptkb:SL(3,ℤ)
|
|
gptkbp:bfsLayer
|
9
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SL(n,ℤ)
|