Finite groups · Family
Small Ree simple groups
Odd extension degree in characteristic 3; q ≥ 27.
Classification coverageFinite simple classification
Parameter domain
Odd extension degree in characteristic 3; q ≥ 27.
| Parameter | Allowed values |
|---|---|
| q | q = 3^(2m+1), integer m ≥ 1 |
Reference properties
Exceptions and identifications
m = 0; q = 3: ²G₂(3)′ ≅ PSL(2,8), with index 3 in ²G₂(3). [sources]
Names and aliases
Ree(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 Ree twisted groups of type ²G₂.
- On the simple groups of Suzuki and ReeSmall Ree construction and simplicity; section 5Open source
family:finite-ree-g2#definitionParameter domain
q: q = 3^(2m+1), integer m ≥ 1
- On the simple groups of Suzuki and ReeSmall Ree construction and simplicity; section 5Open source
family:finite-ree-g2#parametersScope and restrictions
Odd extension degree in characteristic 3; q ≥ 27.
- On the simple groups of Suzuki and ReeSmall Ree construction and simplicity; section 5Open source
family:finite-ree-g2#restrictionExceptions and identifications
m = 0; q = 3: ²G₂(3)′ ≅ PSL(2,8), with index 3 in ²G₂(3).
- Groups with a p-element acting with a single non-trivial Jordan block on a simple module in characteristic pSection 7, seven exceptional isomorphisms before Proposition 24Open source
- Finite simple groups: Lecture 4 — Exceptional groupsSuzuki–Ree groups: small casesOpen source
family:finite-ree-g2#exceptions-1