general linear group GL(n,q)

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:group_of_people gptkb:Lie_group
gptkbp:actsOn	vector space of dimension n over finite field of order q
gptkbp:application	gptkb:geometry coding theory cryptography representation theory
gptkbp:automorphismGroup	outer automorphism group
gptkbp:centralTo	scalar matrices
gptkbp:containsElement	invertible n x n matrices over finite field of order q
gptkbp:definedIn	finite field of order q
gptkbp:hasConnection	true
gptkbp:hasSubgroup	gptkb:special_linear_group_SL(n,q) gptkb:general_linear_group_over_any_field
https://www.w3.org/2000/01/rdf-schema#label	general linear group GL(n,q)
gptkbp:identityElement	identity matrix
gptkbp:isFinite	true
gptkbp:isNonAbelian	n > 1
gptkbp:isQuotientOf	gptkb:center
gptkbp:isReductive	true
gptkbp:isSimple	n > 1, except n=2 and q=2 or 3
gptkbp:namedFor	linear transformations
gptkbp:notation	gptkb:GL(n,q)
gptkbp:operator	matrix multiplication
gptkbp:order	(q^n-1)(q^n-q)...(q^n-q^{n-1})
gptkbp:quotientIs	gptkb:projective_general_linear_group_PGL(n,q)
gptkbp:relatedTo	orthogonal group classical groups
gptkbp:bfsParent	gptkb:SL(n,q) gptkb:special_linear_group_SL(n,q) gptkb:special_orthogonal_group_SO(n,q)
gptkbp:bfsLayer	7