Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
|
| gptkbp:definedIn |
finite field
|
| gptkbp:fullName |
Projective Special Linear Group of degree n over finite field of order q
|
| gptkbp:hasSubgroup |
PGL_n(q)
|
| gptkbp:hasTrivialCenter |
true (for n>2 or q>3)
|
| https://www.w3.org/2000/01/rdf-schema#label |
PSL n(q)
|
| gptkbp:isFamilyOf |
gptkb:finite_simple_groups_of_Lie_type
|
| gptkbp:isNonAbelian |
true (for n>1)
|
| gptkbp:isPerfect |
true (for n>2 or q>3)
|
| gptkbp:isQuotientOf |
gptkb:SL_n(q)
SL_n(q) by its center center of SL_n(q) |
| gptkbp:isSimple |
true (except for (n,q) = (2,2) or (2,3))
|
| gptkbp:notation |
gptkb:PSL_n(q)
|
| gptkbp:order |
q^{n(n-1)/2} \\prod_{i=2}^n (q^i-1)/d, where d=\\gcd(n,q-1)
|
| gptkbp:relatedTo |
orthogonal group
projective group |
| gptkbp:usedIn |
gptkb:geometry
group theory algebraic combinatorics |
| gptkbp:bfsParent |
gptkb:PSL(n,q)
|
| gptkbp:bfsLayer |
6
|