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gptkbp:instanceOf
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gptkb:group_of_people
|
|
gptkbp:abbreviation
|
gptkb:Projective_Special_Linear_Group_of_degree_2
|
|
gptkbp:actsOn
|
projective line
|
|
gptkbp:definedIn
|
SL(2,F)/Z(SL(2,F))
|
|
gptkbp:hasSubgroup
|
gptkb:PGL(2)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
PSL(2)
|
|
gptkbp:importantFor
|
gptkb:algebraic_geometry
gptkb:geometry
group theory
number theory
|
|
gptkbp:is2TransitiveOn
|
projective line
|
|
gptkbp:isCenterless
|
true
|
|
gptkbp:isDefinedOver
|
gptkb:Field
|
|
gptkbp:isFinite
|
finite fields
|
|
gptkbp:isFiniteSimpleGroup
|
for q ≥ 4, q ≠ 2,3
|
|
gptkbp:isInfiniteFor
|
infinite fields
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isomorphicTo
|
A4 (for q=4)
A5 (for q=5)
S4 (for q=9)
|
|
gptkbp:isPerfect
|
true
|
|
gptkbp:isQuotientOf
|
gptkb:SL(2)
|
|
gptkbp:isSimple
|
true
|
|
gptkbp:order
|
q(q^2-1)/gcd(2,q-1) (for finite field F_q)
|
|
gptkbp:relatedTo
|
gptkb:Klein_quartic
gptkb:Fuchsian_groups
gptkb:Möbius_transformations
modular forms
modular group
automorphism group of projective line
|
|
gptkbp:standsFor
|
gptkb:Projective_Special_Linear_Group_of_degree_2
|
|
gptkbp:usedIn
|
classification of finite simple groups
|
|
gptkbp:bfsParent
|
gptkb:SL(2)
|
|
gptkbp:bfsLayer
|
7
|