Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
|
| gptkbp:actsOn |
K^3
|
| gptkbp:centralTo |
scalar matrices in GL(3,K)
|
| gptkbp:defines |
the group of all invertible 3x3 matrices over a field K
|
| gptkbp:fullName |
general linear group of degree 3 over K
|
| gptkbp:hasSubgroup |
GL(n,K) for n>3
SL(3,K) |
| https://www.w3.org/2000/01/rdf-schema#label |
GL(3,K)
|
| gptkbp:identityElement |
matrix inverse
3x3 identity matrix |
| gptkbp:isMatrixGroup |
true
|
| gptkbp:isNonAbelian |
true
|
| gptkbp:isQuotientOf |
gptkb:PGL(3,K)
|
| gptkbp:Lie_algebra |
gl(3,K)
|
| gptkbp:notation |
GL_3(K)
|
| gptkbp:operator |
matrix multiplication
|
| gptkbp:order |
(q^3-1)(q^3-q)(q^3-q^2) if K is a finite field of order q
|
| gptkbp:relatedTo |
determinant
projective general linear group PGL(3,K) special linear group SL(3,K) |
| gptkbp:bfsParent |
gptkb:PGL(3,K)
|
| gptkbp:bfsLayer |
8
|