Geodesic
Ultrasolvability and singularity in the embedding problem
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 25, Tome 414 (2013), pp. 113-126

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We give useful description for representatives of singular solution classes of associated embedding problems over local and global fields. We also discover so-called ultrasolvable embedding problems (i.e., solvable embedding problems which have only fields as solutions), which kernel is not lying in the Frattini group of the covered group. 
@article{ZNSL_2013_414_a6,
     author = {D. D. Kiselev and B. B. Lur'e},
     title = {Ultrasolvability and singularity in the embedding problem},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {113--126},
     publisher = {mathdoc},
     volume = {414},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_414_a6/}
}
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D. D. Kiselev; B. B. Lur'e. Ultrasolvability and singularity in the embedding problem. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 25, Tome 414 (2013), pp. 113-126. http://geodesic.mathdoc.fr/item/ZNSL_2013_414_a6/