group (mathematics)
C51320
concept
A group is a set equipped with a single binary operation that is closed, associative, has an identity element, and in which every element has an inverse.
All labels observed (6)
| Label | Occurrences |
|---|---|
| permutation group | 3 |
| group (mathematics) canonical | 2 |
| symmetric group | 2 |
| Coxeter group | 1 |
| Galois cohomology group | 1 |
| birational transformation 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: group (mathematics)
Generated description
A group is a set equipped with a single binary operation that is closed, associative, has an identity element, and in which every element has an inverse.
Instances (7)
| Instance | Via concept surface |
|---|---|
| Fischer–Griess Monster | — |
| Thompson group Th | — |
| Cremona group of the projective plane | birational transformation group |
| Shafarevich group of a torus | Galois cohomology group |
| PGL(2,7) | permutation group |
| S5 | symmetric group |
| symmetric group S5 | symmetric group |