A note on finite embedding problems with nilpotent kernel
نویسندگان
چکیده
The first aim of this note is to fill a gap in the literature by giving proof following refinement Shafarevich's theorem on solvable Galois groups: Given global field $k$, finite set $\mathcal{S}$ primes and group $G$, there extension $k$ $G$ which all are totally split. To that end, we prove that, given every split embedding problem $G \rightarrow {\rm{Gal}}(L/k)$ over with nilpotent kernel has solution ${\rm{Gal}}(F/k) G$ such $F/L$. We then use contribute inverse theory division rings. Namely, fully describe for automorphisms $\sigma$ acquires skew fractions $k(T, \sigma)$ twisted polynomial ring $k[T, \sigma]$.
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ژورنال
عنوان ژورنال: Journal de Theorie des Nombres de Bordeaux
سال: 2022
ISSN: ['1246-7405', '2118-8572']
DOI: https://doi.org/10.5802/jtnb.1215