|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:actsOn
|
gptkb:vector_space_of_dimension_n_over_F_q
|
|
gptkbp:centralTo
|
set of scalar matrices with determinant 1
|
|
gptkbp:definedIn
|
the group of n x n matrices with determinant 1 over the finite field F_q
|
|
gptkbp:field
|
gptkb:finite_field_F_q
|
|
gptkbp:fullName
|
gptkb:special_linear_group_of_degree_n_over_the_finite_field_with_q_elements
|
|
gptkbp:generation
|
elementary matrices
|
|
gptkbp:hasSubgroup
|
gptkb:GL(n,q)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SL(n,q)
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isPerfect
|
true
|
|
gptkbp:isQuotientOf
|
gptkb:PSL(n,q)
|
|
gptkbp:isSimple
|
false
true (if n>2 or q>3 except (n,q)=(2,2),(2,3))
|
|
gptkbp:notation
|
gptkb:SL_n(q)
|
|
gptkbp:order
|
q^{n(n-1)/2} \\prod_{i=2}^n (q^i-1)
|
|
gptkbp:relatedTo
|
gptkb:general_linear_group_GL(n,q)
gptkb:projective_special_linear_group_PSL(n,q)
orthogonal group
|
|
gptkbp:usedIn
|
gptkb:algebraic_geometry
coding theory
cryptography
number theory
representation theory
finite group theory
|
|
gptkbp:bfsParent
|
gptkb:PSL(n,q)
|
|
gptkbp:bfsLayer
|
6
|