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Embedding problems for automorphism groups of field extensions
Author(s) -
Fehm Arno,
Legrand François,
Paran Elad
Publication year - 2019
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms.12270
Subject(s) - mathematics , embedding , conjecture , embedding problem , automorphism , galois theory , galois group , field (mathematics) , finite field , realization (probability) , pure mathematics , discrete mathematics , algebra over a field , computer science , statistics , artificial intelligence
A central conjecture in inverse Galois theory, proposed by Dèbes 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.