special linear group SL(2n,q)
GPTKB entity
Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:Lie_group |
| gptkbp:actsOn |
2n-dimensional vector space over F_q
|
| gptkbp:centralTo |
set of scalar matrices with determinant 1
|
| gptkbp:containsElement |
2n x 2n matrices with determinant 1 over F_q
|
| gptkbp:definedIn |
finite field of order q
|
| gptkbp:fieldCharacteristic |
characteristic of F_q
|
| gptkbp:generation |
elementary matrices with determinant 1
|
| gptkbp:hasSubgroup |
gptkb:general_linear_group_GL(2n,q)
|
| https://www.w3.org/2000/01/rdf-schema#label |
special linear group SL(2n,q)
|
| gptkbp:isFinite |
true
|
| gptkbp:isNonAbelian |
true (for n>1)
|
| gptkbp:isPerfect |
true (for n>1)
|
| gptkbp:isQuotientOf |
projective special linear group PSL(2n,q)
|
| gptkbp:isSimple |
true (for n>1, q>3 except (n,q)=(2,2),(2,3))
|
| gptkbp:notation |
SL(2n,q)
|
| gptkbp:order |
q^{2n^2-n} \\prod_{i=1}^{2n}(q^i-1)/\\prod_{i=1}^{n}(q^{2i}-1)
|
| gptkbp:relatedTo |
gptkb:general_linear_group_GL(2n,q)
gptkb:special_linear_group_SL(n,q) projective special linear group PSL(2n,q) |
| gptkbp:usedIn |
gptkb:algebraic_geometry
number theory representation theory finite group theory |
| gptkbp:bfsParent |
gptkb:general_linear_group_GL(2n,q)
gptkb:GL(2n,q) |
| gptkbp:bfsLayer |
8
|