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

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

D. D. Kiselev

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

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{https://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
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. D. D. Kiselev, “Metacyclic $2$-extensions with cyclic kernel and the ultrasolvability questions”, J. Math. Sci. (N. Y.), 240:4 (2019), 447–458
2. D. D. Kiselev, “Minimal $p$-extensions and the embedding problem”, Commun. Algebr., 46:1 (2018), 290–321
3. D. D. Kiselev, A. V. Yakovlev, “Ultrasolvable and Sylow extensions with cyclic kernel”, St. Petersburg Math. J., 30:1 (2019), 95–102
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
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