concept in group theory
C30618
concept
A class in group theory is a subset of group elements that are equivalent under conjugation, meaning each element can be written as g⁻¹ag for some fixed a and varying g in the group.
All labels observed (2)
| Label | Occurrences |
|---|---|
| concept in group theory canonical | 2 |
| conjugacy class | 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: concept in group theory
Generated description
A class in group theory is a subset of group elements that are equivalent under conjugation, meaning each element can be written as g⁻¹ag for some fixed a and varying g in the group.
Instances (3)
| Instance | Via concept surface |
|---|---|
|
Fitting
surface form:
Fitting subgroup
|
— |
|
Frattini
surface form:
Frattini subgroup
|
— |
| Frobenius conjugacy class | conjugacy class |