|
gptkbp:instanceOf
|
gptkb:group_of_people
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
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
GL(n,q)
|
|
gptkbp:isAlgebraicGroup
|
true
|
|
gptkbp:isChevalleyGroup
|
true
|
|
gptkbp:isClassicalGroup
|
true
|
|
gptkbp:isFinite
|
true
|
|
gptkbp:isNonAbelian
|
true for n>1
|
|
gptkbp:isParentGroupOf
|
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:algebraic_geometry
gptkb:geometry
gptkb:Galois_theory
coding theory
cryptography
modular forms
number theory
representation theory
combinatorics
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:PGL(n,q)
|
|
gptkbp:bfsLayer
|
7
|