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Izv. RAN. Ser. Mat., 2018, Volume 82, Issue 3, Pages 69–89 (Mi izv8636)  

Ultrasoluble coverings of some nilpotent groups by a cyclic group over number fields and related questions

D. D. Kiselev

All-Russian Academy of International Trade

Abstract: -Let $F$ be a finite nilpotent group of odd order. For every finite cyclic subgroup $A$ of odd order we find necessary and sufficient conditions for a class $h\in H^2(F,A)$ to determine an ultrasoluble extension (under the additional assumption of minimality of all $p$-Sylow subextensions to the extension with class $h$ for all non-Abelian $p$-Sylow subgroups $F_p$ of $F$), that is, for the existence of a Galois extension of number fields $K/k$ with group $F$ such that the corresponding embedding problem is ultrasoluble (it has solutions and all such solutions are fields). We also establish a number of related results.

Keywords: -embedding problem, concordance condition, ultrasolubility, co-embedding problem.

DOI: https://doi.org/10.4213/im8636

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English version:
Izvestiya: Mathematics, 2018, 82:3, 512–531

Bibliographic databases:

UDC: 512.623.32
MSC: 12F12, 11R32, 16K50
Received: 05.12.2016
Revised: 09.04.2017

Citation: D. D. Kiselev, “Ultrasoluble coverings of some nilpotent groups by a cyclic group over number fields and related questions”, Izv. RAN. Ser. Mat., 82:3 (2018), 69–89; Izv. Math., 82:3 (2018), 512–531

Citation in format AMSBIB
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