Statements (29)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
|
| gptkbp:actsOn |
projective line over F
|
| gptkbp:centralTo |
order 2 (for even |F|)
trivial (for odd |F|) |
| gptkbp:definedIn |
field F
|
| gptkbp:fullName |
Projective Special Linear Group of 2x2 matrices over F
|
| gptkbp:hasSubgroup |
PGL(2, F)
|
| https://www.w3.org/2000/01/rdf-schema#label |
PSL(2, F)
|
| gptkbp:isFinite |
true if F is finite
true if F is infinite |
| gptkbp:isNonAbelian |
true (for |F| > 2)
|
| gptkbp:isomorphicTo |
A_4 (if F=F_3)
A_5 (if F=F_5 or F=F_4) S_3 (if F=F_2) |
| gptkbp:isPerfect |
true (for |F| > 3)
|
| gptkbp:isQuotientOf |
gptkb:SL(2,_F)
SL(2, F)/Z(SL(2, F)) center of SL(2, F) |
| gptkbp:isSimple |
true (for |F| > 3)
|
| gptkbp:notation |
PSL_2(F)
|
| gptkbp:order |
|F|(|F|^2-1)/gcd(2,|F|-1)
|
| gptkbp:usedIn |
gptkb:geometry
gptkb:Galois_theory group theory modular forms number theory finite simple group classification |
| gptkbp:bfsParent |
gptkb:SL(2,_F)
|
| gptkbp:bfsLayer |
6
|