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Zap. Nauchn. Sem. POMI, 2016, Volume 452, Pages 108–131 (Mi znsl6359)  

This article is cited in 4 scientific papers (total in 4 papers)

On ultrasolvability of $p$-extensions of an abelian group by a cyclic kernel

D. D. Kiselev

All-Russian Academy of International Trade, Moscow, Russia

Abstract: We solve a problem in the embedding theory by A. V. Yakovlev for $p$-extensions of odd order with cyclic normal subgroup and abelian quotient-group: for such nonsplit extensions there exists a realization for the quotient-group as Galois group over number fields such as corresponding embedding problem is ultrasolvable (i.e. this embedding problem is solvable and has only fields as solutions). Also we give a solution for embedding problems of $p$-extensions of odd order with kernel of order $p$ and with a quotient-group which is represented by direct product of its proper subgroups – this is a generalization for $p>2$ an analogous result for $p=2$ by A. Ledet.

Key words and phrases: ultrasolvability, embedding problem.

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English version:
Journal of Mathematical Sciences (New York), 2018, 232:5, 662–676

Bibliographic databases:

UDC: 512.623.32
Received: 04.07.2016

Citation: D. D. Kiselev, “On ultrasolvability of $p$-extensions of an abelian group by a cyclic kernel”, Problems in the theory of representations of algebras and groups. Part 30, Zap. Nauchn. Sem. POMI, 452, POMI, St. Petersburg, 2016, 108–131; J. Math. Sci. (N. Y.), 232:5 (2018), 662–676

Citation in format AMSBIB
\Bibitem{Kis16}
\by D.~D.~Kiselev
\paper On ultrasolvability of $p$-extensions of an abelian group by a~cyclic kernel
\inbook Problems in the theory of representations of algebras and groups. Part~30
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 452
\pages 108--131
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6359}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3589286}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 232
\issue 5
\pages 662--676
\crossref{https://doi.org/10.1007/s10958-018-3896-8}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85048497646}


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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, “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
    2. D. D. Kiselev, “Minimal $p$-extensions and the embedding problem”, Commun. Algebr., 46:1 (2018), 290–321  crossref  mathscinet  zmath  isi  scopus
    3. A. V. Yakovlev, D. D. Kiselev, “Ultrarazreshimye i silovskie rasshireniya s tsiklicheskim yadrom”, Algebra i analiz, 30:1 (2018), 128–138  mathnet  elib
    4. 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
  • Записки научных семинаров ПОМИ
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