isSemidirectProductOf
P28829
predicate
Indicates that a group is constructed as a semidirect product of two subgroups, where one subgroup acts on the other via automorphisms in a way that generalizes the direct product.
All labels observed (3)
| Label | Occurrences |
|---|---|
| isSemidirectProductOf canonical | 8 |
| semidirectProductOf | 2 |
| hasSemidirectProductDecomposition | 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: isSemidirectProductOf
Generated description
Indicates that a group is constructed as a semidirect product of two subgroups, where one subgroup acts on the other via automorphisms in a way that generalizes the direct product.
Sample triples (11)
| Subject | Object |
|---|---|
| Poincaré group | Lorentz group ⓘ |
| Poincaré group | translation group of Minkowski space ⓘ |
| Euclidean group | orthogonal group O(n) ⓘ |
| Euclidean group | translation group of R^n ⓘ |
| E(n) | O(n) ⓘ |
| E(n) | R^n ⓘ |
| E(n) | R^n ⋊ O(n) via predicate surface "hasSemidirectProductDecomposition" ⓘ |
| ISO(n) | O(n) via predicate surface "semidirectProductOf" ⓘ |
| ISO(n) | R^n via predicate surface "semidirectProductOf" ⓘ |
| affine group of R^n |
GL(n,R)
ⓘ
linked to:
general linear group GL(n,R)
|
| affine group of R^n | R^n ⓘ |