Finite group whose cyclotomic splitting field is a cyclic extension of the rationals
Definition
A finite group whose splitting field is a cyclic extension of the rationals is a finite group with the property that it has a splitting field (for all its irreducible representations) in characteristic zero that is a cyclotomic extension of the rationals and whose Galois group over the rationals is a cyclic group.
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| odd-order p-group | ||||
| rational group | , the field of rational numbers, is a splitting field. |
