Projective Symplectic Group of degree 2n over field of order q
GPTKB entity
Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
|
| gptkbp:actsOn |
2n-dimensional vector space over finite field of order q
|
| gptkbp:alsoKnownAs |
PSp(2n, q)
|
| gptkbp:centralTo |
Symplectic Group of degree 2n over field of order q
|
| gptkbp:hasSubgroup |
Projective General Linear Group of degree 2n over field of order q
|
| https://www.w3.org/2000/01/rdf-schema#label |
Projective Symplectic Group of degree 2n over field of order q
|
| gptkbp:isChevalleyGroup |
true
|
| gptkbp:isClassicalGroup |
true
|
| gptkbp:isFinite |
true
|
| gptkbp:isNonAbelian |
true
|
| gptkbp:isQuotientOf |
center of Sp(2n, q)
Symplectic Group of degree 2n over field of order q |
| gptkbp:isSimple |
n > 1 and q > 2
true for n > 1 and (n, q) ≠ (2, 2), (2, 3) |
| gptkbp:notation |
gptkb:PSp_{2n}(q)
|
| gptkbp:order |
q^{n^2} * \\prod_{i=1}^n (q^{2i} - 1) / gcd(2, q-1)
|
| gptkbp:preserves |
non-degenerate alternating bilinear form
|
| gptkbp:relatedTo |
Symplectic Group Sp(2n, q)
|
| gptkbp:usedIn |
gptkb:algebraic_geometry
representation theory finite group theory |
| gptkbp:bfsParent |
gptkb:PSp(2n,q)
|
| gptkbp:bfsLayer |
6
|