Geodesic
Ultrasoluble coverings of some nilpotent groups by a~cyclic group
Izvestiya. Mathematics , Tome 82 (2018) no. 3, pp. 512-531

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-Let $F$ be a finite nilpotent group of odd order. For every finite cyclic subgroup $A$ of odd order we find necessary and sufficient conditions for a class $h\in H^2(F,A)$ to determine an ultrasoluble extension (under the additional assumption of minimality of all $p$-Sylow subextensions to the extension with class $h$ for all non-Abelian $p$-Sylow subgroups $F_p$ of $F$), that is, for the existence of a Galois extension of number fields $K/k$ with group $F$ such that the corresponding embedding problem is ultrasoluble (it has solutions and all such solutions are fields). We also establish a number of related results.
Keywords: -embedding problem, ultrasolubility, co-embedding problem.
Mots-clés : concordance condition 
@article{IM2_2018_82_3_a3,
     author = {D. D. Kiselev},
     title = {Ultrasoluble coverings of some nilpotent groups by a~cyclic group},
     journal = {Izvestiya. Mathematics },
     pages = {512--531},
     publisher = {mathdoc},
     volume = {82},
     number = {3},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2018_82_3_a3/}
}
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D. D. Kiselev. Ultrasoluble coverings of some nilpotent groups by a~cyclic group. Izvestiya. Mathematics , Tome 82 (2018) no. 3, pp. 512-531. http://geodesic.mathdoc.fr/item/IM2_2018_82_3_a3/