Geodesic
The embedding problem with kernel $\mathrm{PSL}\,(2,p^2)$
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 16, Tome 349 (2007), pp. 135-145 
V. V. Ishkhanov; B. B. Lur'e. The embedding problem with kernel $\mathrm{PSL}\,(2,p^2)$. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 16, Tome 349 (2007), pp. 135-145. http://geodesic.mathdoc.fr/item/ZNSL_2007_349_a3/
@article{ZNSL_2007_349_a3,
     author = {V. V. Ishkhanov and B. B. Lur'e},
     title = {The embedding problem with kernel $\mathrm{PSL}\,(2,p^2)$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {135--145},
     year = {2007},
     volume = {349},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_349_a3/}
}
TY  - JOUR
AU  - V. V. Ishkhanov
AU  - B. B. Lur'e
TI  - The embedding problem with kernel $\mathrm{PSL}\,(2,p^2)$
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2007
SP  - 135
EP  - 145
VL  - 349
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2007_349_a3/
LA  - ru
ID  - ZNSL_2007_349_a3
ER  - 
%0 Journal Article
%A V. V. Ishkhanov
%A B. B. Lur'e
%T The embedding problem with kernel $\mathrm{PSL}\,(2,p^2)$
%J Zapiski Nauchnykh Seminarov POMI
%D 2007
%P 135-145
%V 349
%U http://geodesic.mathdoc.fr/item/ZNSL_2007_349_a3/
%G ru
%F ZNSL_2007_349_a3

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The embedding problem of number fields is considered. It is proved that it is solvable if and only if all the associated local problems at the infinite points are solvable. It is also proved that the solvability of an adjoint with Sylow 2-group is equivalent to the solvability of the original problem.

[1] V. V. Ishkhanov, B. B. Lure, “Zadacha pogruzheniya nad $p$-rasshireniem”, Algebra i analiz, 9:4 (1997), 87–97 | MR | Zbl

[2] B. B. Lure, “K zadache pogruzheniya s yadrom bez tsentra”, Izv. AN SSSR, Ser. mat., 28:5 (1964), 1135–1138 | MR

[3] R. Steinberg, Lektsii o gruppakh Shevalle, Mir, M., 1975 | MR | Zbl

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

[5] S. P. Demushkin, I. R. Shafarevich, “Vtoroe prepyatstvie dlya zadachi pogruzheniya polei algebraicheskikh chisel”, Izv. AN SSSR, Ser. mat., 26:6 (1962), 911–924 | MR | Zbl

[6] S. P. Demushkin, I. R. Shafarevich, “Zadacha pogruzheniya dlya lokalnykh polei”, Izv. AN SSSR, Ser. mat., 23:6 (1959), 823–840 | Zbl