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Zap. Nauchn. Sem. POMI, 2013, Volume 414, Pages 113–126 (Mi znsl5669)  

This article is cited in 9 scientific papers (total in 9 papers)

Ultrasolvability and singularity in the embedding problem

D. D. Kiseleva, B. B. Lur'eb

a Lomonosov Moscow State University, Moscow, Russia
b St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia

Abstract: 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.

Key words and phrases: ultrasolvable embedding problem, singular solutions.

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English version:
Journal of Mathematical Sciences (New York), 2014, 199:3, 306–312

UDC: 512
Received: 15.01.2013

Citation: D. D. Kiselev, B. B. Lur'e, “Ultrasolvability and singularity in the embedding problem”, Problems in the theory of representations of algebras and groups. Part 25, Zap. Nauchn. Sem. POMI, 414, POMI, St. Petersburg, 2013, 113–126; J. Math. Sci. (N. Y.), 199:3 (2014), 306–312

Citation in format AMSBIB
\Bibitem{KisLur13}
\by D.~D.~Kiselev, B.~B.~Lur'e
\paper Ultrasolvability and singularity in the embedding problem
\inbook Problems in the theory of representations of algebras and groups. Part~25
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 414
\pages 113--126
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5669}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2014
\vol 199
\issue 3
\pages 306--312
\crossref{https://doi.org/10.1007/s10958-014-1858-3}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84902332928}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. D. Kiselev, “Ultrasolvable covering of the group $Z_2$ by the groups $Z_8$, $Z_{16}$ and $Q_8$”, J. Math. Sci. (N. Y.), 219:4 (2016), 523–538  mathnet  crossref  mathscinet
    2. A. V. Yakovlev, “Ultrasolvable embedding problem for number fields”, St. Petersburg Math. J., 27:6 (2016), 1049–1051  mathnet  crossref  mathscinet  isi  elib
    3. D. D. Kiselev, “On ultrasolvable embedding problems with cyclic kernel”, Russian Math. Surveys, 71:6 (2016), 1149–1151  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. D. D. Kiselev, “On ultrasolvability of $p$-extensions of an abelian group by a cyclic kernel”, J. Math. Sci. (N. Y.), 232:5 (2018), 662–676  mathnet  crossref  mathscinet
    5. D. D. Kiselev, I. A. Chubarov, “On ultrasolvability of some classes of minimal non-split $p$-extensions with cyclic kernel for $p>2$”, J. Math. Sci. (N. Y.), 232:5 (2018), 677–692  mathnet  crossref  mathscinet
    6. D. D. Kiselev, “Metacyclic $2$-extensions with cyclic kernel and the ultrasolvability questions”, J. Math. Sci. (N. Y.), 240:4 (2019), 447–458  mathnet  crossref
    7. D. D. Kiselev, “Minimal $p$-extensions and the embedding problem”, Commun. Algebr., 46:1 (2018), 290–321  crossref  mathscinet  zmath  isi  scopus
    8. D. D. Kiselev, A. V. Yakovlev, “Ultrasolvable and Sylow extensions with cyclic kernel”, St. Petersburg Math. J., 30:1 (2019), 95–102  mathnet  crossref  mathscinet  isi  elib
    9. D. D. Kiselev, “Ultrasoluble coverings of some nilpotent groups by a cyclic group over number fields and related questions”, Izv. Math., 82:3 (2018), 512–531  mathnet  crossref  crossref  adsnasa  isi  elib
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