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Zap. Nauchn. Sem. POMI, 2015, Volume 435, Pages 47–72 (Mi znsl6151)  

This article is cited in 3 scientific papers (total in 3 papers)

Ultrasolvable covering of the group $Z_2$ by the groups $Z_8$, $Z_{16}$ and $Q_8$

D. D. Kiselev

All-Russian Academy of International Trade, Moscow, Russia

Abstract: 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.

Key words and phrases: ultrasolvability, embedding problem.

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English version:
Journal of Mathematical Sciences (New York), 2016, 219:4, 523–538

Bibliographic databases:

UDC: 512.623
Received: 21.04.2015

Citation: D. D. Kiselev, “Ultrasolvable covering of the group $Z_2$ by the groups $Z_8$, $Z_{16}$ and $Q_8$”, Problems in the theory of representations of algebras and groups. Part 28, Zap. Nauchn. Sem. POMI, 435, POMI, St. Petersburg, 2015, 47–72; J. Math. Sci. (N. Y.), 219:4 (2016), 523–538

Citation in format AMSBIB
\Bibitem{Kis15}
\by D.~D.~Kiselev
\paper Ultrasolvable covering of the group $Z_2$ by the groups $Z_8$, $Z_{16}$ and~$Q_8$
\inbook Problems in the theory of representations of algebras and groups. Part~28
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 435
\pages 47--72
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6151}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3493617}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 219
\issue 4
\pages 523--538
\crossref{https://doi.org/10.1007/s10958-016-3125-2}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. D. D. Kiselev, “Metatsiklicheskie $2$-rasshireniya s tsiklicheskim yadrom i voprosy ultrarazreshimosti”, Voprosy teorii predstavlenii algebr i grupp. 32, Zap. nauchn. sem. POMI, 460, POMI, SPb., 2017, 114–133  mathnet
    3. D. D. Kiselev, “Minimal $p$-extensions and the embedding problem”, Commun. Algebr., 46:1 (2018), 290–321  crossref  mathscinet  zmath  isi  scopus
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