Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
|
| gptkbp:actsOn |
2n-dimensional vector space
|
| gptkbp:definedIn |
finite field of order q
|
| gptkbp:dimensions |
2n
|
| gptkbp:fullName |
gptkb:projective_symplectic_group
|
| gptkbp:hasSubgroup |
PGL_{2n}(q)
|
| https://www.w3.org/2000/01/rdf-schema#label |
PSp {2n}(q)
|
| gptkbp:isFinite |
true
|
| gptkbp:isQuotientOf |
gptkb:Sp_{2n}(q)
center of Sp_{2n}(q) symplectic group Sp_{2n}(q) |
| gptkbp:isSimple |
true
|
| gptkbp:isSimpleException |
n=1 or (n=2 and q=2)
|
| gptkbp:notation |
gptkb:PSp_{2n}(q)
PSymp(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:relatedGroup |
symplectic transformations
|
| gptkbp:relatedTo |
gptkb:Chevalley_groups
classical groups |
| gptkbp:type |
gptkb:Lie_type_C_n
|
| gptkbp:bfsParent |
gptkb:PSp(2n,q)
|
| gptkbp:bfsLayer |
6
|