Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
classical group |
| gptkbp:actsOn |
2n-dimensional vector space
|
| gptkbp:centralTo |
cyclic group of order gcd(2,q-1)
|
| gptkbp:definedIn |
finite field of order q
|
| gptkbp:foundIn |
finite group theory
|
| gptkbp:hasSubgroup |
gptkb:general_linear_group_GL(2n,q)
|
| https://www.w3.org/2000/01/rdf-schema#label |
symplectic group Sp(n,q)
|
| gptkbp:isNonAbelian |
true
|
| gptkbp:isPerfect |
true (for n>1, q>2)
|
| gptkbp:isSimple |
true (for n>1, q>2)
|
| gptkbp:notation |
gptkb:Sp(2n,q)
|
| gptkbp:order |
q^{n^2} \\prod_{i=1}^n (q^{2i}-1)
|
| gptkbp:preserves |
non-degenerate alternating bilinear form
|
| gptkbp:relatedTo |
projective symplectic group PSp(n,q)
|
| gptkbp:type |
gptkb:Lie_type_C_n
|
| gptkbp:usedIn |
gptkb:algebraic_geometry
gptkb:quantum_information_theory coding theory representation theory |
| gptkbp:bfsParent |
gptkb:orthogonal_group_O(n,q)
|
| gptkbp:bfsLayer |
8
|