projective general linear group PGL(n,q)

URI: https://gptkb.org/entity/projective_general_linear_group_PGL(n,q)
GPTKB entity
Statements (24)
Predicate Object
gptkbp:instanceOf gptkb:group_of_people
orthogonal group
gptkbp:actsOn projective space of dimension n-1 over finite field of order q
gptkbp:automorphismGroup projective space of dimension n-1 over finite field of order q
gptkbp:builtBy gptkb:general_linear_group_GL(n,q)
quotienting GL(n,q) by its center
gptkbp:centralTo trivial
gptkbp:contains gptkb:projective_special_linear_group_PSL(n,q)
gptkbp:definedIn finite field of order q
gptkbp:hasSubgroup gptkb:PSL(n,q)
https://www.w3.org/2000/01/rdf-schema#label projective general linear group PGL(n,q)
gptkbp:isQuotientOf gptkb:GL(n,q)
gptkb:projective_semilinear_group_PΓL(n,q)
gptkbp:isSimple false
gptkbp:notation gptkb:PGL(n,q)
gptkbp:order (q^n-1)(q^n-q)...(q^n-q^{n-1})/(q-1)
gptkbp:relatedTo gptkb:projective_special_linear_group_PSL(n,q)
gptkbp:usedIn gptkb:geometry
group theory
gptkbp:bfsParent gptkb:general_linear_group_GL(n,q)
gptkb:projective_special_linear_group_PSL(n,q)
gptkb:projective_symplectic_group_PSp(2n,q)
gptkb:GL(n,q)
gptkbp:bfsLayer 8