What the study found
The authors show that, under the stated condition, algebraic number fields can be constructed with degree larger than the size of the automorphism group that fixes the base field. A special case given in the abstract says that if the Inverse Galois problem for Q has a solution for a finite group G of order n, then algebraic number fields of degree nm exist for any m ≥ 3 with the same automorphism group G.
Why the authors say this matters
The study suggests a way to measure how large the degree of such an extension can be compared with the order of its automorphism group. The authors frame this as an objective tied to a weaker form of the Inverse Galois Problem, which concerns realizing a finite group as a group of field automorphisms fixing a base field.
What the researchers tested
The paper studies inflated G-extensions for algebraic number fields. It builds on earlier work by Legrand and Paran for Hilbertian fields and finite groups, and on earlier work by M. Fried for Q. The abstract does not give further methodological details.
What worked and what didn't
The abstract states that a special case of the authors' result works when the Inverse Galois problem for Q has a solution for a finite group G of order n. In that case, the authors say there are algebraic number fields of degree nm for any m ≥ 3 with the same automorphism group G.
What to keep in mind
The abstract does not describe limitations, proof details, or conditions beyond the stated special case. It also does not say how the construction behaves outside the cases mentioned in the summary.
Key points
- The paper studies inflated G-extensions for algebraic number fields.
- It addresses a weaker form of the Inverse Galois Problem for Hilbertian fields and finite groups.
- A special case says that if the Inverse Galois problem for Q has a solution for a finite group G of order n, then fields of degree nm exist for any m ≥ 3 with automorphism group G.
- The abstract links the work to earlier results by Legrand and Paran, and by M. Fried for Q.
Disclosure
- Research title:
- Algebraic number fields can realize inflated G-extensions
- Authors:
- M Krithika, P Vanchinathan
- Publication date:
- 2026-04-24
- OpenAlex record:
- View
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