Plus-type even orthogonal finite simple groups
n ≥ 4; plus type has Witt index n.
The projective Ω group of a nondegenerate split quadratic form on Fq^(2n).
Definition sourcesParameter domain
n ≥ 4; plus type has Witt index n.
| Parameter | Allowed values |
|---|---|
| n | integer n ≥ 4 |
| q | q = p^f, with p prime and f ≥ 1 |
Reference properties
Exceptions and identifications
dimension 4: PΩ⁺(4,q) ≅ PSL(2,q) × PSL(2,q), so this is not a new simple family. [sources]
dimension 6: PΩ⁺(6,q) ≅ PSL(4,q); use the linear family. [sources]
Names and aliases
Dₙ(q) · O₂ₙ⁺(q)
Claims and sources
Each assertion has a stable identifier within this record and a source locator or derivation. Cite the dataset edition when referring to a corrected or historical claim.
Definition
The projective Ω group of a nondegenerate split quadratic form on Fq^(2n).
- Classical groups: detailed lecture notesSections 3.4–3.5, plus type and projective Ω groupsOpen source
family:finite-even-orthogonal-plus#definitionParameter domain
n: integer n ≥ 4; q: q = p^f, with p prime and f ≥ 1
- Classical groups: detailed lecture notesSections 3.4–3.5, plus type and projective Ω groupsOpen source
family:finite-even-orthogonal-plus#parametersScope and restrictions
n ≥ 4; plus type has Witt index n.
- Classical groups: detailed lecture notesSections 3.4–3.5, plus type and projective Ω groupsOpen source
family:finite-even-orthogonal-plus#restrictionExceptions and identifications
dimension 4: PΩ⁺(4,q) ≅ PSL(2,q) × PSL(2,q), so this is not a new simple family.
- Finite simple groups: Lecture 3 — Classical groupsSmall-dimensional orthogonal groupsOpen source
family:finite-even-orthogonal-plus#exceptions-1Exceptions and identifications
dimension 6: PΩ⁺(6,q) ≅ PSL(4,q); use the linear family.
- Finite simple groups: Lecture 3 — Classical groupsSmall-dimensional orthogonal groupsOpen source
family:finite-even-orthogonal-plus#exceptions-2