symplectic group over finite fields

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:algebraic_geometry gptkb:group_of_people
gptkbp:actsOn	gptkb:Vector
gptkbp:centralTo	cyclic group of order gcd(2, q-1)
gptkbp:class	Dynkin diagram C_n
gptkbp:field	finite field
gptkbp:hasConnection	true
gptkbp:hasMaximalSubgroup	gptkb:general_linear_group
gptkbp:hasOuterAutomorphisms	true
gptkbp:hasSubgroup	gptkb:general_linear_group
gptkbp:hasType	gptkb:C_n
https://www.w3.org/2000/01/rdf-schema#label	symplectic group over finite fields
gptkbp:isChevalleyGroup	true
gptkbp:isDefinedOver	gptkb:finite_field_F_q
gptkbp:isFiniteSimpleGroup	for n > 1, q > 2
gptkbp:isLieTypeGroup	true
gptkbp:isNonAbelian	true
gptkbp:isPerfect	true for n > 1
gptkbp:isQuotientOf	general symplectic group
gptkbp:isReductive	true
gptkbp:isSimple	n > 1, q > 2
gptkbp:isSplit	true
gptkbp:isTransitiveOn	isotropic subspaces Lagrangian subspaces
gptkbp:notation	Sp(2n, F_q)
gptkbp:order	q^{n^2} \\prod_{i=1}^n (q^{2i}-1)
gptkbp:preserves	symplectic form
gptkbp:relatedTo	gptkb:projective_symplectic_group orthogonal group
gptkbp:usedIn	gptkb:algebraic_geometry gptkb:quantum_information_theory coding theory modular forms representation theory Galois representations finite group theory
gptkbp:bfsParent	gptkb:sp(n)
gptkbp:bfsLayer	8