subgroup
C17168
concept
A subgroup is a subset of a group that is itself a group under the same binary operation, containing the identity, inverses, and being closed under the operation.
All labels observed (10)
| Label | Occurrences |
|---|---|
| subgroup canonical | 4 |
| Bantoid subgroup | 2 |
| series of subgroups | 2 |
| Clifford group subgroup | 1 |
| characteristic subgroup | 1 |
| discrete subgroup of PSL(2,R) | 1 |
| modular group | 1 |
| rotation group | 1 |
| subgroup invariant | 1 |
| subgroup of Möbius transformations | 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: subgroup
Generated description
A subgroup is a subset of a group that is itself a group under the same binary operation, containing the identity, inverses, and being closed under the operation.
Instances (14)
| Instance | Via concept surface |
|---|---|
| The 6s | — |
| Lie subgroup | — |
| Northern Bantoid | Bantoid subgroup |
|
modular group PSL(2,Z)
surface form:
PSL(2,ℤ)
|
modular group |
|
rotation group SO(3)
surface form:
SO(3)
|
rotation group |
| Dreamers | — |
| Kleinian group | subgroup of Möbius transformations |
| (2,3,7) triangle group | discrete subgroup of PSL(2,R) |
| Fitting subgroup | subgroup invariant |
| Fitting series | series of subgroups |
| North Bantoid | Bantoid subgroup |
| Pauli group | Clifford group subgroup |
| Pasi | — |
| Zassenhaus filtration | series of subgroups |