|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:orthogonal_group
|
|
gptkbp:actsOn
|
vector space of dimension n over finite field with q elements
|
|
gptkbp:automorphismGroup
|
gptkb:vector_space_of_dimension_n_over_F_q
|
|
gptkbp:centralTo
|
scalar matrices
|
|
gptkbp:contains
|
gptkb:SL(n,q)
|
|
gptkbp:definedIn
|
finite field with q elements
|
|
gptkbp:fullName
|
general linear group of degree n over the finite field with q elements
|
|
gptkbp:hasConnection
|
true
|
|
gptkbp:hasNormalSubgroup
|
gptkb:center
gptkb:SL(n,q)
|
|
gptkbp:hasSubgroup
|
gptkb:special_linear_group_SL(n,q)
gptkb:projective_general_linear_group_PGL(n,q)
GL(n,K) for any field K containing F_q
|
|
gptkbp:isAlgebraicGroup
|
true
|
|
gptkbp:isChevalleyGroup
|
true
|
|
gptkbp:isClassicalGroup
|
true
|
|
gptkbp:isFinite
|
true
|
|
gptkbp:isNonAbelian
|
true for n>1
|
|
gptkbp:isParentGroupOf
|
gptkb:orthogonal_group
|
|
gptkbp:isQuotientOf
|
center isomorphic to PGL(n,q)
|
|
gptkbp:isReductive
|
true
|
|
gptkbp:isSimple
|
false for n>1, q>3
|
|
gptkbp:notation
|
GL_n(q)
|
|
gptkbp:order
|
(q^n-1)(q^n-q)...(q^n-q^{n-1})
|
|
gptkbp:relatedGroup
|
invertible n x n matrices over F_q
|
|
gptkbp:usedIn
|
gptkb:combinatorics
gptkb:algebraic_geometry
gptkb:geometry
gptkb:Galois_theory
coding theory
cryptography
modular forms
number theory
representation theory
algebraic groups
algebraic combinatorics
design theory
finite fields
finite group theory
group cohomology
group actions
permutation groups
finite projective geometry
|
|
gptkbp:bfsParent
|
gptkb:SL(n,q)
gptkb:SO(n,q)
gptkb:general_linear_group_GL(n,q)
|
|
gptkbp:bfsLayer
|
10
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
GL(n,q)
|