Statements (21)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
|
| gptkbp:actsOn |
projective plane over K
|
| gptkbp:automorphismGroup |
projective plane over K
|
| gptkbp:contains |
PSL_3(K) as a normal subgroup
|
| gptkbp:definedIn |
gptkb:field_K
|
| gptkbp:fullName |
projective general linear group of degree 3 over K
|
| gptkbp:hasSubgroup |
PGL_n(K) for n>3
|
| https://www.w3.org/2000/01/rdf-schema#label |
PGL 3(K)
|
| gptkbp:isFinite |
true if K is finite
true if K is infinite |
| gptkbp:isMatrixGroup |
true
|
| gptkbp:isNonAbelian |
true
|
| gptkbp:isProjectiveGroup |
true
|
| gptkbp:isQuotientOf |
GL_3(K)
SL_3(K) by its center center of GL_3(K) |
| gptkbp:isSimple |
true (if K is not of order 2 or 3)
|
| gptkbp:order |
(q^3-1)(q^3-q)(q^3-q^2)/(q-1)(q^2-1)(q^3-1) for finite field K=F_q
|
| gptkbp:relatedTo |
gptkb:geometry
|
| gptkbp:bfsParent |
gptkb:PGL(3,K)
|
| gptkbp:bfsLayer |
8
|