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gptkbp:instanceOf
|
gptkb:group_of_people
projective linear group
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|
gptkbp:actsOn
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projective space of dimension n-1 over F
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|
gptkbp:centralTo
|
trivial if n > 2 and F is algebraically closed
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|
gptkbp:contains
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PSL(n, F) as a normal subgroup if n > 2 and F not of characteristic 2
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gptkbp:definedIn
|
field F
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|
gptkbp:describes
|
group of projective transformations of projective space
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|
gptkbp:fullName
|
projective general linear group
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|
gptkbp:homomorphismFrom
|
gptkb:GL(n,_F)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
PGL(n, F)
|
|
gptkbp:isomorphicTo
|
Aut(P^{n-1}(F))
|
|
gptkbp:isQuotientOf
|
gptkb:GL(n,_F)
center of GL(n, F)
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|
gptkbp:isSimple
|
n > 2 and F not of characteristic 2
|
|
gptkbp:notation
|
gptkb:PGL(n,_F)
gptkb:PGL_n(F)
|
|
gptkbp:order
|
(q^n-1)(q^n-q)...(q^n-q^{n-1})/(q-1) if F is finite field of order q
|
|
gptkbp:parameter
|
F
n
|
|
gptkbp:relatedTo
|
gptkb:PSL(n,_F)
|
|
gptkbp:usedIn
|
gptkb:algebraic_geometry
gptkb:geometry
group theory
|
|
gptkbp:bfsParent
|
gptkb:GL(n,_F)
gptkb:special_linear_Lie_algebra
gptkb:projective_general_linear_group
gptkb:projective_linear_group
|
|
gptkbp:bfsLayer
|
6
|