projective general linear group
GPTKB entity
Statements (26)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebra
gptkb:group_of_people |
| gptkbp:abbreviation |
gptkb:PGL(n,_F)
|
| gptkbp:actsOn |
gptkb:geometry
|
| gptkbp:category |
gptkb:group_of_people
gptkb:Lie_group classical group quotient group |
| gptkbp:centralTo |
trivial
|
| gptkbp:defines |
the quotient of the general linear group GL(n, F) by its center
|
| gptkbp:field |
gptkb:mathematics
group theory |
| gptkbp:for_n=2_over_finite_field_F_q |
order is q(q^2-1)
|
| gptkbp:isNotSimpleFor |
n=2 and |F|=2 or 3
|
| gptkbp:isQuotientOf |
gptkb:general_linear_group
|
| gptkbp:isSimple |
n>2 and |F|>3
|
| gptkbp:notation |
gptkb:PGL(n,_F)
|
| gptkbp:order |
(q^n-1)(q^n-q)...(q^n-q^{n-1})/(q-1)
|
| gptkbp:relatedTo |
gptkb:general_linear_group
projective special linear group projective linear group |
| gptkbp:usedIn |
gptkb:algebraic_geometry
gptkb:geometry finite group theory |
| gptkbp:bfsParent |
gptkb:general_linear_group
|
| gptkbp:bfsLayer |
5
|