group
C11692
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 (8)
| Label | Occurrences |
|---|---|
| group canonical | 12 |
| Gruppe | 1 |
| class of groups | 1 |
| group completion | 1 |
| group nickname | 1 |
| group presentation technique | 1 |
| group under composition | 1 |
| triangle 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
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 (19)
| Instance | Via concept surface |
|---|---|
| Lie group | — |
| Grothendieck group | group completion |
| (2,3,7) triangle group | triangle group |
| Wirtinger presentation of knot groups | group presentation technique |
|
Bright
surface form:
Philhellenes
|
— |
| The Dogs | group nickname |
| Chevalley groups | class of groups |
| Guppees | — |
|
Abelian groups
surface form:
Abelian group
|
— |
| PSL(2,ℤ/Nℤ) | — |
| SL(2,ℤ) | — |
| McL | — |
| Cremona group of the projective plane | group under composition |
| Witt group of quadratic forms | — |
| Brauer group | — |
| Wolfpack | — |
| II./JG 2 | Gruppe |
| Picard group | — |
|
PSL(2,\mathbb{C})
surface form:
PSL(2,ℂ)
|
— |