projective linear group PGL(N+1, K)
GPTKB entity
Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebraic_geometry
gptkb:group_of_people |
| gptkbp:actsOn |
projective space of dimension N over K
|
| gptkbp:automorphismGroup |
gptkb:geometry
|
| gptkbp:centralTo |
trivial
|
| gptkbp:definedIn |
gptkb:field_K
|
| https://www.w3.org/2000/01/rdf-schema#label |
projective linear group PGL(N+1, K)
|
| gptkbp:isFinite |
finite field K
|
| gptkbp:isInfiniteFor |
infinite field K
|
| gptkbp:isMatrixGroup |
yes
|
| gptkbp:isomorphicTo |
Aut(P^N(K))
|
| gptkbp:isQuotientOf |
scalar matrices
general linear group GL(N+1, K) |
| gptkbp:isSimple |
N > 1 and K not too small
|
| gptkbp:notation |
PGL(N+1, K)
|
| gptkbp:order |
(q^{N+1}-1)(q^{N+1}-q)...(q^{N+1}-q^N)/(q-1)
|
| gptkbp:originatedIn |
gptkb:algebraic_geometry
gptkb:geometry group theory |
| gptkbp:relatedTo |
projective special linear group PSL(N+1, K)
|
| gptkbp:bfsParent |
gptkb:projective_space_P^N
|
| gptkbp:bfsLayer |
7
|