Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
|
| gptkbp:actsOn |
gptkb:geometry
|
| gptkbp:automorphismGroup |
projective space P^{n-1}(F)
|
| gptkbp:centralTo |
trivial
|
| gptkbp:definedIn |
field F
|
| gptkbp:fullName |
projective general linear group
|
| gptkbp:hasSubgroup |
PSL_n(F)
|
| https://www.w3.org/2000/01/rdf-schema#label |
PGL n(F)
|
| gptkbp:isAlgebraicGroup |
true
|
| gptkbp:isMatrixGroup |
true
|
| gptkbp:isomorphicTo |
Aut(P^{n-1}(F))
|
| gptkbp:isQuotientOf |
GL_n(F)
center of GL_n(F) |
| gptkbp:isSimple |
true (for n>2 and F not too small)
|
| gptkbp:notation |
gptkb:PGL_n(F)
|
| gptkbp:order |
(q^n-1)(q^n-q)...(q^n-q^{n-1})/(q-1)(q^2-1)...(q^n-1) (for finite field F=F_q)
|
| gptkbp:relatedTo |
PSL_n(F)
|
| gptkbp:usedIn |
gptkb:algebraic_geometry
gptkb:geometry group theory |
| gptkbp:bfsParent |
gptkb:PGL(n,_F)
|
| gptkbp:bfsLayer |
7
|