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Embedding problems for automorphism groups of field extensions
- Publication Year :
- 2018
- Publisher :
- arXiv, 2018.
-
Abstract
- A central conjecture in inverse Galois theory, proposed by D\`{e}bes and Deschamps, asserts that every finite split embedding problem over an arbitrary field can be regularly solved. We give an unconditional proof of a consequence of this conjecture, namely that such embedding problems can be regularly solved if one waives the requirement that the solution fields are normal. This extends previous results of M. Fried, Takahashi, Deschamps, and the last two authors concerning the realization of finite groups as automorphism groups of field extensions.
- Subjects :
- Pure mathematics
Conjecture
Mathematics - Number Theory
General Mathematics
010102 general mathematics
Galois theory
Field (mathematics)
Automorphism
01 natural sciences
Embedding problem
Field extension
FOS: Mathematics
Embedding
Number Theory (math.NT)
0101 mathematics
Realization (systems)
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....b6c8596a18032f207b2dc7662a6d4b58
- Full Text :
- https://doi.org/10.48550/arxiv.1812.10819