finite simple group
C7459
concept
A finite simple group is a finite group that has no nontrivial normal subgroups, meaning its only normal subgroups are the trivial group and the group itself.
All labels observed (7)
| Label | Occurrences |
|---|---|
| finite simple group canonical | 18 |
| Conway group | 3 |
| perfect group | 3 |
| non-abelian simple group | 1 |
| non‑abelian simple group | 1 |
| projective special linear group | 1 |
| simple group | 1 |
Description generation (CDg)
The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.
Instruction
generate a one-sentence description for a given conceptual class. # Response Format Return only the sentence: "Description: [one-sentence description of the conceptional class]"
Input
Class: finite simple group
Generated description
A finite simple group is a finite group that has no nontrivial normal subgroups, meaning its only normal subgroups are the trivial group and the group itself.
Instances (18)
| Instance | Via concept surface |
|---|---|
| Co1 | — |
| Co2 | — |
| Monster group | — |
| Co3 | — |
| PSL(2,7) | — |
|
Conway group Co1
linked to:
Conway groups
|
— |
| Fischer–Griess Monster | — |
| M | — |
| Fischer group Fi24′ | — |
| Held group | — |
| McLaughlin group | — |
| Thompson group Th | — |
| Janko group J4 | — |
|
Monster group
linked to:
monstrous moonshine
|
— |
| Harada–Norton group | — |
| McL | — |
| SL(2,7) | perfect group |
| symmetric group S5 | simple group |