special linear group SL(n,q)

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:group_of_people gptkb:Lie_group
gptkbp:actsOn	vector space of dimension n over field of order q
gptkbp:centralTo	scalar matrices with determinant 1
gptkbp:containsElement	n x n matrices
gptkbp:definedIn	finite field of order q
gptkbp:elementsHaveDeterminant	1
gptkbp:finiteIf	q is finite
gptkbp:generation	elementary matrices
gptkbp:hasSubgroup	gptkb:general_linear_group_GL(n,q)
https://www.w3.org/2000/01/rdf-schema#label	special linear group SL(n,q)
gptkbp:infiniteIf	q is infinite
gptkbp:isSimple	n >= 2, (n,q) ≠ (2,2), (2,3)
gptkbp:namedAfter	orthogonal group
gptkbp:notation	gptkb:SL(n,q)
gptkbp:order	q^{n^2-1} * product_{k=2}^n (q^k-1)
gptkbp:relatedGroup	matrix multiplication
gptkbp:relatedTo	gptkb:projective_special_linear_group_PSL(n,q)
gptkbp:studiedBy	gptkb:Ferdinand_Georg_Frobenius
gptkbp:usedIn	gptkb:algebraic_geometry gptkb:geometry group theory number theory representation theory
gptkbp:bfsParent	gptkb:Chevalley_groups
gptkbp:bfsLayer	6