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gptkbp:instanceOf
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gptkb:group_of_people
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gptkbp:actsOn
|
projective space of dimension n-1 over F_q
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|
gptkbp:builtBy
|
gptkb:SL(n,q)
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gptkbp:category
|
orthogonal group
classical group
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|
gptkbp:centralTo
|
trivial for most n,q
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|
gptkbp:definedIn
|
PSL(n,q) = SL(n,q)/Z(SL(n,q))
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gptkbp:finiteSimpleGroupClassification
|
appears as infinite family
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gptkbp:fullName
|
gptkb:Projective_Special_Linear_Group
|
|
gptkbp:hasSubgroup
|
gptkb:PGL(n,q)
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|
https://www.w3.org/2000/01/rdf-schema#label
|
PSL(n,q)
|
|
gptkbp:isNonAbelian
|
true for n > 2 or q > 3
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gptkbp:isomorphicTo
|
A_5 for PSL(2,4) and PSL(2,5)
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|
gptkbp:isQuotientOf
|
center of SL(n,q)
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|
gptkbp:isSimple
|
true, except for (n,q) = (2,2), (2,3)
|
|
gptkbp:notation
|
gptkb:Projective_Special_Linear_Group
gptkb:PSL_n(q)
|
|
gptkbp:order
|
q^{n(n-1)/2} \\prod_{i=2}^n (q^i-1)/d, where d = gcd(n,q-1)
|
|
gptkbp:parameter
|
n (integer > 1)
q (prime power)
|
|
gptkbp:relatedTo
|
gptkb:Weyl_group
Lie type group
|
|
gptkbp:usedIn
|
gptkb:algebraic_geometry
gptkb:Galois_theory
finite group theory
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gptkbp:bfsParent
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gptkb:Weyl_group
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gptkbp:bfsLayer
|
5
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