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

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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. 
@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},
     publisher = {mathdoc},
     volume = {349},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_349_a3/}
}
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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/