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},
year = {2013},
volume = {414},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_414_a6/}
}
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/
[1] V. V. Ishkhanov, B. B. Lure, D. K. Faddeev, Zadacha pogruzheniya v teorii Galua, Nauka, M., 1990 | MR | Zbl
[2] V. V. Ishkhanov, B. B. Lure, “Zadacha pogruzheniya nad $p$-rasshireniem”, Algebra i Analiz, 9:4 (1997), 57–97 | MR | Zbl
[3] Ch. Kertis, I. Rainer, Teoriya predstavlenii konechnykh grupp i assotsiativnykh algebr, Nauka, M., 1969 | MR
[4] B. B. Lure, “Ob universalno razreshimykh zadachakh pogruzheniya”, Tr. MIAN, 183, 1990, 121–126 | MR | Zbl
[5] S. A. Syskin, “Abstraktnye svoistva prostykh sporadicheskikh grupp”, UMN, 35:5 (1980), 181–212 | MR | Zbl
[6] S. Maklein, Gomologiya, Mir, M., 1966