lecture-notes
Finite simple groups: Lecture 4 — Exceptional groups
Robert A. Wilson
Use in this reference: Linked for verification. No redistribution licence is asserted; this dataset contains original summaries and selected mathematical facts, not source tables.
Relevant material: Ten exceptional families; Suzuki–Ree parameters and small cases; G2
Dependent assertions
| Record | Assertion | Source locator |
|---|---|---|
| G₂(q) | Definition | G₂(q), order and simplicity |
| G₂(q) | Parameter domain | G₂(q), order and simplicity |
| G₂(q) | Scope and restrictions | G₂(q), order and simplicity |
| G₂(q) | Exceptions and identifications | G₂(q), small case |
| F₄(q) | Definition | Ten exceptional families |
| F₄(q) | Parameter domain | Ten exceptional families |
| F₄(q) | Scope and restrictions | Ten exceptional families |
| E₆(q) | Definition | Ten exceptional families |
| E₆(q) | Parameter domain | Ten exceptional families |
| E₆(q) | Scope and restrictions | Ten exceptional families |
| E₇(q) | Definition | Ten exceptional families |
| E₇(q) | Parameter domain | Ten exceptional families |
| E₇(q) | Scope and restrictions | Ten exceptional families |
| E₈(q) | Definition | Ten exceptional families |
| E₈(q) | Parameter domain | Ten exceptional families |
| E₈(q) | Scope and restrictions | Ten exceptional families |
| ²E₆(q) | Definition | Ten exceptional families |
| ²E₆(q) | Parameter domain | Ten exceptional families |
| ²E₆(q) | Scope and restrictions | Ten exceptional families |
| ³D₄(q) | Definition | Ten exceptional families |
| ³D₄(q) | Parameter domain | Ten exceptional families |
| ³D₄(q) | Scope and restrictions | Ten exceptional families |
| ²B₂(q) | Exceptions and identifications | Suzuki–Ree groups: small cases |
| ²G₂(q) | Exceptions and identifications | Suzuki–Ree groups: small cases |
| ²F₄(q) | Exceptions and identifications | Suzuki–Ree groups: small cases |
| ²F₄(q) | Tits derived subgroup | Suzuki–Ree groups: small cases |
| Sporadic | Exceptions and identifications | Suzuki–Ree small cases |
| Suz | Reference scope | Suzuki families |
| ²F₄(2)′ | Definition | Suzuki–Ree small cases |
| ²F₄(2)′ | Simple | Suzuki–Ree small cases |
| ²F₄(2)′ | Abelian | Simple Tits group of composite order |
| ²F₄(2)′ | Classification convention | Suzuki–Ree small cases |
| ²F₄(2)′ | Derived small case of ²F₄ | Suzuki–Ree small cases |