lecture-notes
Finite simple groups: Lecture 1 — Introduction and alternating 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: CFSG statement and alternating groups, slides 1–4
Dependent assertions
| Record | Assertion | Source locator |
|---|---|---|
| Cₚ | Definition | Simple groups, first slide |
| Cₚ | Parameter domain | Simple groups, first slide |
| Cₚ | Scope and restrictions | Simple groups, first slide |
| Cₚ | Order | CFSG statement, first slide |
| Cₚ | Conventions and use | Simple groups, first slide |
| Cₚ | Prime-order cyclic subfamily | CFSG statement, first slide |
| Aₙ | Definition | CFSG; even permutations; simplicity of Aₙ |
| Aₙ | Parameter domain | CFSG; even permutations; simplicity of Aₙ |
| Aₙ | Scope and restrictions | CFSG; even permutations; simplicity of Aₙ |
| Aₙ | Order | Even permutations |
| Sporadic | Definition | CFSG statement |
| Sporadic | Parameter domain | CFSG statement |
| Sporadic | Scope and restrictions | CFSG statement |
| Sₙ | Definition | Permutations; even permutations |
| Sₙ | Parameter domain | Permutations; even permutations |
| Sₙ | Scope and restrictions | Permutations; even permutations |
| Sₙ | Conventions and use | Even permutations; simplicity of alternating groups |
| M₁₁ | Abelian | CFSG statement, first slide |
| M₁₂ | Abelian | CFSG statement, first slide |
| M₂₂ | Abelian | CFSG statement, first slide |
| M₂₃ | Abelian | CFSG statement, first slide |
| M₂₄ | Abelian | CFSG statement, first slide |
| J₁ | Abelian | CFSG statement, first slide |
| J₂ | Abelian | CFSG statement, first slide |
| J₃ | Abelian | CFSG statement, first slide |
| J₄ | Abelian | CFSG statement, first slide |
| Co₁ | Abelian | CFSG statement, first slide |
| Co₂ | Abelian | CFSG statement, first slide |
| Co₃ | Abelian | CFSG statement, first slide |
| Fi₂₂ | Abelian | CFSG statement, first slide |
| Fi₂₃ | Abelian | CFSG statement, first slide |
| Fi₂₄′ | Abelian | CFSG statement, first slide |
| HS | Abelian | CFSG statement, first slide |
| McL | Abelian | CFSG statement, first slide |
| He | Abelian | CFSG statement, first slide |
| Ru | Abelian | CFSG statement, first slide |
| Suz | Abelian | CFSG statement, first slide |
| O’N | Abelian | CFSG statement, first slide |
| HN | Abelian | CFSG statement, first slide |
| Ly | Abelian | CFSG statement, first slide |
| Th | Abelian | CFSG statement, first slide |
| B | Abelian | CFSG statement, first slide |
| M | Abelian | CFSG statement, first slide |