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Zap. Nauchn. Sem. POMI, 2017, Volume 460, Pages 114–133 (Mi znsl6473)  

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

D. D. Kiselev

All-Russian Academy of International Trade, Moscow, Russia

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.

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English version:
Journal of Mathematical Sciences (New York), 2019, 240:4, 447–458

UDC: 512.623.32
Received: 05.10.2017

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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