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Embedding problems for automorphism groups of field extensions

Authors :
Arno Fehm
François Legrand
Elad Paran
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.

Details

Database :
OpenAIRE
Accession number :
edsair.doi.dedup.....b6c8596a18032f207b2dc7662a6d4b58
Full Text :
https://doi.org/10.48550/arxiv.1812.10819