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Zapiski Nauchnykh Seminarov POMI, 2017, Volume 460, Pages 114–133 (Mi znsl6473)  
This article is cited in 1 scientific paper (total in 1 paper)

Metacyclic $2$-extensions with cyclic kernel and the ultrasolvability questions

D. D. Kiselev

All-Russian Academy of International Trade, Moscow, Russia
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Abstract: We give a necessary and sufficient conditions for $2$-local ultrasolvability of the metacyclic extensions. Then we derive the ultrasolvability for an arbibrary group extension, which has a local ultrasolvable associated subextension of the second type. Finally, using the above reductions, we establish the ultrasolvability results for a wide class of non-split $2$-extensions with cyclic kernel.
Key words and phrases: ultrasolvability, embedding problem, metacyclic extensions.
Received: 05.10.2017
English version:
Journal of Mathematical Sciences (New York), 2019, Volume 240, Issue 4, Pages 447–458
DOI: https://doi.org/10.1007/s10958-019-04362-2
Document Type: Article
UDC: 512.623.32
Language: Russian
Citation: D. D. Kiselev, “Metacyclic $2$-extensions with cyclic kernel and the ultrasolvability questions”, Problems in the theory of representations of algebras and groups. Part 32, Zap. Nauchn. Sem. POMI, 460, POMI, St. Petersburg, 2017, 114–133; J. Math. Sci. (N. Y.), 240:4 (2019), 447–458
Citation in format AMSBIB
\Bibitem{Kis17}
\by D.~D.~Kiselev
\paper Metacyclic $2$-extensions with cyclic kernel and the ultrasolvability questions
\inbook Problems in the theory of representations of algebras and groups. Part~32
\serial Zap. Nauchn. Sem. POMI
\yr 2017
\vol 460
\pages 114--133
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6473}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2019
\vol 240
\issue 4
\pages 447--458
\crossref{https://doi.org/10.1007/s10958-019-04362-2}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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