Embedding problems for automorphism groups of field extensions. Issue 4 (13th June 2019)

• Record Type: Journal Article
• Authors: Fehm, Arno; Legrand, François; Paran, Elad
• Is Part Of: Bulletin of the London Mathematical Society. Volume 51:Issue 4(2019)
• Page Start: 732
• Page End: 744
• Publication Date: 2019-06-13
• Subjects: 12E25 -- 12E30 -- 12F12 -- 20B25 (primary); Mathematics -- Periodicals; 510
• DOI: 10.1112/blms.12270
• Languages: English
• ISSNs: 0024-6093

Abstract

Abstract: 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.