Embedding problems for automorphism groups of field extensions

Arno Fehm; François Legrand; Elad Paran

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arXiv · 1812.10819

Embedding problems for automorphism groups of field extensions

Arno Fehm·François Legrand·Elad Paran

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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.

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Arno Fehm, François Legrand, Elad Paran. 2018-12-27. Embedding problems for automorphism groups of field extensions. https://arxiv.org/abs/1812.10819

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