Geodesic
Ultrasolvable covering of the group $Z_2$ by the groups $Z_8$, $Z_{16}$ and $Q_8$
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 28, Tome 435 (2015), pp. 47-72 Cet article a éte moissonné depuis la source Math-Net.Ru

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We construct infinite series of non-trivial ultrasolvable embedding problems with cyclic kernel of order $8,16$ and quaternion kernel of order $8$. Moreover, we discover $2$-local non-split universally solvable embedding problems of a quadratic extension into a Galois algebra whose kernel is generalized quaternion or cyclic. 
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     title = {Ultrasolvable covering of the group $Z_2$ by the groups $Z_8$, $Z_{16}$ and~$Q_8$},
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}
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D. D. Kiselev. Ultrasolvable covering of the group $Z_2$ by the groups $Z_8$, $Z_{16}$ and $Q_8$. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 28, Tome 435 (2015), pp. 47-72. http://geodesic.mathdoc.fr/item/ZNSL_2015_435_a3/

[1] V. V. Ishkhanov, “O polupryamoi zadache pogruzheniya s nilpotentnym yadrom”, Izv. AN SSSR. Ser. mat., 40:1 (1976), 3–25 | MR | Zbl

[2] D. D. Kiselev, “Primery zadach pogruzheniya, u kotorykh resheniya tolko polya”, UMN, 68:4 (2013), 181–182 | DOI | MR | Zbl

[3] D. D. Kiselev, B. B. Lure, “Ultrarazreshimost i singulyarnost v probleme pogruzheniya”, Zap. nauchn. sem. POMI, 414, 2013, 113–126

[4] V. V. Ishkhanov, B. B. Lure, D. K. Faddeev, Zadacha pogruzheniya v teorii Galua, Nauka, M., 1990 | MR

[5] A. V. Yakovlev, “Zadacha pogruzheniya polei”, Izv. AN SSSR. Ser. mat., 28:3 (1964), 645–660 | MR | Zbl

[6] A. V. Yakovlev, “Zadacha pogruzheniya dlya chislovykh polei”, Izv. AN SSSR, Cer. mat., 31:2 (1967), 211–224 | MR | Zbl

[7] V. V. Ishkhanov, B. B. Lure, “Uslovie soglasnosti dlya zadachi pogruzheniya s $p$-rasshireniem”, Zap. nauchn. sem. POMI, 236, 1997, 100–105 | MR | Zbl

[8] D. K. Faddeev, “Ob odnoi gipoteze Khasse”, DAN SSSR, 94:6 (1954), 1013–1016 | MR

[9] G. Malle, B. H. Matzat, Inverse Galois theory, Springer-Verlag, N.Y., 1999 | MR | Zbl

[10] B. B. Lure, “Ob universalno razreshimykh zadachakh pogruzheniya”, Tr. MIAN, 183, 1990, 121–126 | MR | Zbl

[11] V. V. Ishkhanov, B. B. Lure, “Universalno razreshimye zadachi pogruzheniya s tsiklicheskim yadrom”, Zap. nauchn. sem. POMI, 265, 1999, 189–197 | MR | Zbl

[12] V. V. Ishkhanov, B. B. Lure, “Universalnaya zadacha pogruzheniya s tsiklicheskim yadrom poryadka 8”, Zap. nauchn. sem. POMI, 281, 2001, 210–220 | MR | Zbl

[13] V. V. Ishkhanov, B. B. Lure, “Ob universalno razreshimykh zadachakh pogruzheniya s tsiklicheskim yadrom”, Zap. nauchn. sem. POMI, 338, 2006, 173–179 | MR | Zbl

[14] S. A. Syskin, “Abstraktnye svoistva prostykh sporadicheskikh grupp”, UMN, 35:5 (1980), 181–212 | MR | Zbl