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gptkbp:instanceOf
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gptkb:algebra
gptkb:group_of_people
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gptkbp:actsOn
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gptkb:geometry
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gptkbp:centralTo
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trivial (in most cases)
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gptkbp:definedIn
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quotient of SL(n, F) by its center
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gptkbp:example
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gptkb:PSL(2,_7)
gptkb:PSL(3,_2)
PSL(2, 5) ≅ A5
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gptkbp:fullName
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gptkb:Projective_Special_Linear_Group
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gptkbp:hasSubgroup
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gptkb:PGL(n,_F)
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|
https://www.w3.org/2000/01/rdf-schema#label
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PSL(n, F)
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gptkbp:importantFor
|
gptkb:geometry
group theory
algebraic groups
finite group theory
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gptkbp:isChevalleyGroup
|
true
|
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gptkbp:isFinite
|
true (if F is finite)
true (if F is infinite)
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gptkbp:isNonAbelian
|
true (for n > 2 or |F| > 3)
|
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gptkbp:isPerfect
|
true (for n > 2 or |F| > 3)
|
|
gptkbp:isQuotientOf
|
gptkb:SL(n,_F)
|
|
gptkbp:isSimple
|
true (for n > 2 and most fields F)
|
|
gptkbp:notation
|
gptkb:PSL(n,_F)
|
|
gptkbp:order
|
|PSL(n, q)| = |SL(n, q)| / |Z(SL(n, q))| (for F = finite field of order q)
|
|
gptkbp:originatedIn
|
gptkb:geometry
linear transformations
|
|
gptkbp:parameter
|
F
n
|
|
gptkbp:relatedTo
|
gptkb:SL(n,_F)
|
|
gptkbp:usedIn
|
classification of finite simple groups
|
|
gptkbp:bfsParent
|
gptkb:projective_special_linear_group
|
|
gptkbp:bfsLayer
|
6
|