Geodesic
On embedding problem with cyclic kernel for number fields
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 23, Tome 400 (2012), pp. 208-214

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It is proved that for number fields an embedding problem with cyclic kernel has a solution if 2 completely decomposes in the embeddable field and the consistency condition holds. 
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     author = {A. V. Yakovlev},
     title = {On embedding problem with cyclic kernel for number fields},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {208--214},
     publisher = {mathdoc},
     volume = {400},
     year = {2012},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_400_a10/}
}
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A. V. Yakovlev. On embedding problem with cyclic kernel for number fields. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 23, Tome 400 (2012), pp. 208-214. http://geodesic.mathdoc.fr/item/ZNSL_2012_400_a10/