hasNormalSubgroup
P63683
predicate
Indicates that one group is a normal subgroup of another group, meaning it is invariant under conjugation by elements of the larger group.
All labels observed (5)
| Label | Occurrences |
|---|---|
| hasNormalSubgroup canonical | 5 |
| isNormalSubgroupOf | 3 |
| hasMinimalNormalSubgroup | 1 |
| hasSimpleNormalSubgroup | 1 |
| normalSubgroup | 1 |
Description generation (PDg)
The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.
Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning. # Instructions Focus on describing the relationship, not the entities themselves. # Response Format Begin the description with \' Indicates...\'
Input
Predicate: hasNormalSubgroup
Generated description
Indicates that one group is a normal subgroup of another group, meaning it is invariant under conjugation by elements of the larger group.
Sample triples (11)
| Subject | Object |
|---|---|
| E(n) | translation group R^n ⓘ |
|
SO(3)
linked to:
rotation group SO(3)
|
O(3)
via predicate surface "isNormalSubgroupOf"
ⓘ
linked to:
orthogonal group O(n)
|
| ISO(n) | R^n via predicate surface "normalSubgroup" ⓘ |
| affine group of R^n | translation subgroup R^n ⓘ |
|
SL(n,ℝ)
linked to:
special linear group SL(n,R)
|
GL(n,ℝ)
via predicate surface "isNormalSubgroupOf"
ⓘ
linked to:
general linear group GL(n,R)
|
|
SL(n,ℂ)
linked to:
special linear group SL(n,C)
|
GL(n,ℂ)
via predicate surface "isNormalSubgroupOf"
ⓘ
linked to:
general linear group GL(n,C)
|
| PGL(2,7) | PSL(2,7) ⓘ |
| PGL(2,7) | PSL(2,7) via predicate surface "hasSimpleNormalSubgroup" ⓘ |
| PGL(2,7) | PSL(2,7) via predicate surface "hasMinimalNormalSubgroup" ⓘ |
| S5 | A5 ⓘ |
| symmetric group S5 | alternating group A5 ⓘ |