special linear group of degree n over the finite field with q elements
URI: https://gptkb.org/entity/special_linear_group_of_degree_n_over_the_finite_field_with_q_elements
GPTKB entity
Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
|
| gptkbp:actsOn |
gptkb:vector_space_of_dimension_n_over_F_q
|
| gptkbp:alsoKnownAs |
SL(n, F_q)
|
| gptkbp:category |
gptkb:Lie_group
|
| gptkbp:centralTo |
scalar matrices with determinant 1
|
| gptkbp:definedIn |
group of n x n matrices with determinant 1 over F_q
|
| gptkbp:field |
finite field with q elements
|
| gptkbp:generation |
elementary matrices with determinant 1
|
| gptkbp:hasNormalSubgroup |
gptkb:center
|
| gptkbp:hasSubgroup |
general linear group of degree n over the finite field with q elements
|
| https://www.w3.org/2000/01/rdf-schema#label |
special linear group of degree n over the finite field with q elements
|
| gptkbp:isPerfect |
true for n > 2 or (n = 2 and q > 3)
|
| gptkbp:isQuotientOf |
projective special linear group PSL(n, q)
|
| gptkbp:isSimple |
n > 2 or (n = 2 and q > 3)
|
| gptkbp:notation |
SL(n, q)
|
| gptkbp:order |
q^{n^2-1} * (q^n-1)(q^{n-1}-1)...(q-1)/ (q-1)
|
| gptkbp:usedIn |
gptkb:algebraic_geometry
gptkb:geometry group theory representation theory |
| gptkbp:bfsParent |
gptkb:SL(n,q)
|
| gptkbp:bfsLayer |
7
|