Geodesic
Around Podewski's conjecture
Krzysztof Krupiński 1   ; Predrag Tanović 2   ; Frank O. Wagner 3
1 Instytut Matematyczny Uniwersytet Wrocławski Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland
2 Mathematical Institute SANU Belgrade, Serbia
3 Université de Lyon, CNRS Université Lyon 1 Institut Camille Jordan, UMR 5208 43 bd du 11 novembre 1918 69622 Villeurbanne Cedex, France
Fundamenta Mathematicae, Tome 222 (2013) no. 2, pp. 175-193 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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A long-standing conjecture of Podewski states that every minimal field is algebraically closed. Known in positive characteristic, it remains wide open in characteristic zero. We reduce Podewski's conjecture to the (partially) ordered case, and we conjecture that such fields do not exist. We prove the conjecture in case the incomparability relation is transitive (the almost linear case). We also study minimal groups with a (partial) order, and give a complete classification of almost linear minimal groups as certain valued groups.
DOI : 10.4064/fm222-2-4
Keywords: long standing conjecture podewski states every minimal field algebraically closed known positive characteristic remains wide characteristic zero reduce podewskis conjecture partially ordered conjecture fields exist prove conjecture incomparability relation transitive almost linear study minimal groups partial order complete classification almost linear minimal groups certain valued groups

Krzysztof Krupiński  1   ; Predrag Tanović  2   ; Frank O. Wagner  3

1 Instytut Matematyczny Uniwersytet Wrocławski Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland
2 Mathematical Institute SANU Belgrade, Serbia
3 Université de Lyon, CNRS Université Lyon 1 Institut Camille Jordan, UMR 5208 43 bd du 11 novembre 1918 69622 Villeurbanne Cedex, France 
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Krzysztof Krupiński; Predrag Tanović; Frank O. Wagner. Around Podewski's conjecture. Fundamenta Mathematicae, Tome 222 (2013) no. 2, pp. 175-193. doi: 10.4064/fm222-2-4

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