unitsFormGroupIsomorphicTo
P27190
predicate
Indicates that the group formed by the units (invertible elements) of one algebraic structure is isomorphic, as a group, to the group formed by the units of another structure.
All labels observed (4)
| Label | Occurrences |
|---|---|
| hasUnitGroup | 2 |
| unitGroupOfRingOfIntegers | 1 |
| unitGroupOrderInGaussianIntegers | 1 |
| unitsFormGroupIsomorphicTo canonical | 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: unitsFormGroupIsomorphicTo
Generated description
Indicates that the group formed by the units (invertible elements) of one algebraic structure is isomorphic, as a group, to the group formed by the units of another structure.
Sample triples (5)
| Subject | Object |
|---|---|
| Gaussian integers | cyclic group of order 4 ⓘ |
|
cyclotomic fields
surface form:
cyclotomic field
|
Dirichlet unit group of rank φ(n)/2−1 for n>2 via predicate surface "hasUnitGroup" ⓘ |
| i | 4 via predicate surface "unitGroupOrderInGaussianIntegers" ⓘ |
| Gaussian rationals ℚ(i) | {±1,±i} via predicate surface "unitGroupOfRingOfIntegers" ⓘ |
| Hurwitz quaternions | binary tetrahedral group via predicate surface "hasUnitGroup" NERFINISHED ⓘ |