projective symplectic group PSp(2n,q)
GPTKB entity
Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
classical group simple group |
| gptkbp:actsOn |
projective space of dimension 2n-1
|
| gptkbp:centralTo |
trivial (for most q, n>1)
|
| gptkbp:definedIn |
finite field of order q
|
| gptkbp:dimensions |
2n
|
| https://www.w3.org/2000/01/rdf-schema#label |
projective symplectic group PSp(2n,q)
|
| gptkbp:isomorphicTo |
Sp(2n,q)/Z(Sp(2n,q))
|
| gptkbp:isQuotientOf |
gptkb:symplectic_group_Sp(2n,q)
center of Sp(2n,q) |
| gptkbp:isSimple |
true (for n>1 or q>2)
|
| gptkbp:notation |
gptkb:PSp(2n,q)
PSP_{2n}(q) |
| gptkbp:order |
q^{n^2} * \\prod_{i=1}^n (q^{2i}-1)/gcd(2,q-1)
|
| gptkbp:originatedIn |
gptkb:symplectic_group_Sp(2n,q)
|
| gptkbp:preserves |
symplectic form
|
| gptkbp:relatedTo |
gptkb:projective_general_linear_group_PGL(n,q)
gptkb:projective_orthogonal_group |
| gptkbp:usedIn |
classification of finite simple groups
finite group theory |
| gptkbp:bfsParent |
gptkb:Sp(2n,q)
gptkb:symplectic_group_Sp(2n,q) |
| gptkbp:bfsLayer |
7
|