hasIsometryGroup
P14251
predicate
Indicates that one entity possesses or is associated with a particular isometry group describing all distance-preserving transformations of that entity.
All labels observed (14)
| Label | Occurrences |
|---|---|
| hasAutomorphismGroup | 18 |
| automorphismGroup | 15 |
| isIsometryGroupOf | 8 |
| hasIsometryGroup canonical | 7 |
| isometryGroupOf | 4 |
| symmetryGroupType | 3 |
| isSpacetimeSymmetryGroupOf | 2 |
| hasFullIsometryGroup | 1 |
| hasInvariantGroup | 1 |
| hasOrientationPreservingIsometryGroup | 1 |
| isHomogeneousSpaceFor | 1 |
| isometryGroup | 1 |
| isometryType | 1 |
| matchesSymmetryGroupOf | 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: hasIsometryGroup
Generated description
Indicates that one entity possesses or is associated with a particular isometry group describing all distance-preserving transformations of that entity.
Sample triples (64)
| Subject | Object |
|---|---|
| de Sitter spacetime | SO(1,4) ⓘ |
| Reissner–Nordström metric | R × SO(3) ⓘ |
| Euclidean space | E(n) ⓘ |
|
Leech lattice
linked to:
Conway groups
|
automorphism group of the Leech lattice
via predicate surface "hasAutomorphismGroup"
ⓘ
linked to:
Conway groups
|
| Platonic solids | finite rotation groups via predicate surface "symmetryGroupType" ⓘ |
| Klein quartic | PSL(2,7) via predicate surface "automorphismGroup" ⓘ |
| Klein quartic | projective special linear group of 2x2 matrices over field with 7 elements via predicate surface "automorphismGroup" ⓘ |
| Weyl’s gauge theory | local symmetry via predicate surface "symmetryGroupType" ⓘ |
| Weyl’s gauge theory | gauge group via predicate surface "symmetryGroupType" ⓘ |
| Euclidean group | distance-preserving transformations via predicate surface "isometryType" ⓘ |
| Euclidean group | Euclidean space as E(n)/O(n) via predicate surface "isHomogeneousSpaceFor" ⓘ |
| E(n) | R^n via predicate surface "isIsometryGroupOf" ⓘ |
| Fermat curve | large finite group depending on n via predicate surface "hasAutomorphismGroup" ⓘ |
| anti-de Sitter space | SO(2,d-1) ⓘ |
| anti-de Sitter space |
O(2,d-1)
ⓘ
linked to:
AdS isometry group SO(2,d)
|
| AdS isometry group SO(2,d) | (d+1)-dimensional anti-de Sitter space via predicate surface "isIsometryGroupOf" ⓘ |
| AdS isometry group SO(2,d) | (d+1)-dimensional anti-de Sitter space via predicate surface "isSpacetimeSymmetryGroupOf" ⓘ |
| AdS isometry group SO(2,d) |
AdS_{d+1}
via predicate surface "isometryGroupOf"
ⓘ
linked to:
anti-de Sitter space
|
| AdS isometry group SO(2,d) |
AdS_{d+1}
via predicate surface "isSpacetimeSymmetryGroupOf"
ⓘ
linked to:
anti-de Sitter space
|
| AdS isometry group SO(2,d) | d-dimensional conformal field theory via predicate surface "matchesSymmetryGroupOf" ⓘ |
| AdS isometry group SO(2,d) | maximally symmetric space with negative curvature via predicate surface "isometryGroupOf" ⓘ |
| Co1 |
Co1·2
via predicate surface "hasAutomorphismGroup"
ⓘ
linked to:
Co1
|
| Leech lattice |
Conway group Co0
via predicate surface "automorphismGroup"
ⓘ
linked to:
Conway groups
|
| Leech lattice |
Conway group Co1
via predicate surface "automorphismGroup"
ⓘ
linked to:
Conway groups
|
| Leech lattice |
Conway group Co2
via predicate surface "automorphismGroup"
ⓘ
linked to:
Co3
|
| Leech lattice |
Conway group Co3
via predicate surface "automorphismGroup"
ⓘ
linked to:
Conway groups
|
| Monster group | itself via predicate surface "hasAutomorphismGroup" ⓘ |
| Co3 | Co3 via predicate surface "hasAutomorphismGroup" ⓘ |
|
SO(3)
linked to:
rotation group SO(3)
|
oriented Euclidean 3-space fixing the origin via predicate surface "isometryGroupOf" ⓘ |
| Riemann sphere | Möbius transformations via predicate surface "automorphismGroup" ⓘ |
| Riemann sphere | fractional linear transformations via predicate surface "automorphismGroup" ⓘ |
| PSL(2,7) | PGL(2,7) via predicate surface "automorphismGroup" ⓘ |
| Fano plane |
PGL(3,2)
via predicate surface "hasAutomorphismGroup"
ⓘ
linked to:
PSL(2,7)
|
|
Clebsch diagonal surface
linked to:
Clebsch diagonal surfaces
|
symmetric group S5 via predicate surface "hasAutomorphismGroup" ⓘ |
| ISO(n) |
Euclidean n-space
via predicate surface "isometryGroupOf"
ⓘ
linked to:
Euclidean space
|
| orthogonal group O(n) | standard Euclidean space R^n fixing the origin via predicate surface "isIsometryGroupOf" ⓘ |
| orthogonal group O(n+1,2) | quadratic space of signature (n+1,2) via predicate surface "isIsometryGroupOf" ⓘ |
| SO(2,d-1) | d-dimensional anti-de Sitter space via predicate surface "isIsometryGroupOf" ⓘ |
| Spin(2,d) | spin structure on AdS_{d+1} via predicate surface "isIsometryGroupOf" ⓘ |
| Spin(2,d) | a space of signature (2,d) at the spin level via predicate surface "isIsometryGroupOf" ⓘ |
| GF(p) | trivial (only identity) via predicate surface "hasAutomorphismGroup" ⓘ |
| extended binary Golay code | Mathieu group M24 via predicate surface "automorphismGroup" ⓘ |
| E8 lattice |
Weyl group of type E8
via predicate surface "automorphismGroup"
ⓘ
linked to:
Weyl group
|
|
extended binary Golay code
linked to:
Golay code
|
Mathieu group M24 via predicate surface "automorphismGroup" ⓘ |
|
binary Golay code
linked to:
Golay code
|
Mathieu group M23 via predicate surface "automorphismGroup" ⓘ |
|
ternary Golay code
linked to:
Golay code
|
Mathieu group M11 via predicate surface "automorphismGroup" ⓘ |
| Fischer–Griess Monster | itself via predicate surface "hasAutomorphismGroup" ⓘ |
| Griess algebra | Monster group via predicate surface "hasAutomorphismGroup" ⓘ |
| McLaughlin group |
McL:2
via predicate surface "hasAutomorphismGroup"
ⓘ
linked to:
McL
|
| Thompson group Th | Thompson group Th via predicate surface "hasAutomorphismGroup" ⓘ |