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gptkbp:instanceOf
|
gptkb:group_of_people
modular group
|
|
gptkbp:actsOn
|
ℤ^n
|
|
gptkbp:centralTo
|
{I, -I} for n = 2
{I} for n > 2
|
|
gptkbp:containsElement
|
n×n matrices with integer entries and determinant 1
|
|
gptkbp:definedIn
|
the group of n×n integer matrices with determinant 1
|
|
gptkbp:for_n=1
|
trivial group
|
|
gptkbp:for_n=2
|
modular group
non-abelian
generated by elementary matrices
has congruence subgroups
important in modular forms
|
|
gptkbp:for_n=3
|
related to geometry of numbers
used in crystallography
|
|
gptkbp:for_n>1
|
non-abelian
|
|
gptkbp:fullName
|
special linear group over the integers
|
|
gptkbp:hasCongruenceSubgroups
|
true
|
|
gptkbp:hasFiniteIndexSubgroups
|
true
|
|
gptkbp:hasInfiniteOrderElements
|
true
|
|
gptkbp:hasKazhdanPropertyT
|
true for n ≥ 3
|
|
gptkbp:hasProperty
|
discrete subgroup of SL(n, ℝ)
|
|
gptkbp:hasSubgroup
|
GL(n, ℤ)
|
|
gptkbp:hasTorsionElements
|
true
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SL(n, ℤ)
|
|
gptkbp:isAlgebraicGroup
|
true
|
|
gptkbp:isCountable
|
true
|
|
gptkbp:isDiscrete
|
true in SL(n, ℝ)
|
|
gptkbp:isFinite
|
true
|
|
gptkbp:isFinitelyGenerated
|
true
|
|
gptkbp:isLatticeIn
|
gptkb:SL(n,_ℝ)
|
|
gptkbp:isMatrixGroup
|
true
|
|
gptkbp:isPerfect
|
true for n ≥ 3
|
|
gptkbp:isQuotientOf
|
PSL(n, ℤ)
|
|
gptkbp:isResiduallyFinite
|
true
|
|
gptkbp:isSimple
|
false
|
|
gptkbp:notation
|
SL(n, Z)
|
|
gptkbp:usedIn
|
gptkb:geometry
gptkb:topology
gptkb:algebraic_K-theory
crystallography
group theory
modular forms
number theory
representation theory
lattice theory
automorphic forms
|
|
gptkbp:bfsParent
|
gptkb:orthogonal_group
|
|
gptkbp:bfsLayer
|
5
|