abelian group
C28301
concept
An abelian group is a set equipped with an associative binary operation that has an identity element and inverses for every element, and for which the operation is commutative.
All labels observed (4)
| Label | Occurrences |
|---|---|
| abelian group canonical | 3 |
| abstract algebraic structure | 2 |
| Witt group | 1 |
| trivial 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: abelian group
Generated description
An abelian group is a set equipped with an associative binary operation that has an identity element and inverses for every element, and for which the operation is commutative.
Instances (7)
| Instance | Via concept surface |
|---|---|
| Grothendieck group | — |
|
special orthogonal group SO(n)
surface form:
SO(1)
|
trivial group |
| U(1) | — |
| Harada–Norton group | abstract algebraic structure |
| Witt group of quadratic forms | Witt group |
| idèle class group | — |
| S5 | abstract algebraic structure |