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Zapiski Nauchnykh Seminarov POMI, 1994, Volume 211, Pages 120–126
(Mi znsl5882)
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On the embedding problem with non-Abelian kernel of order $p^4$. IV
V. V. Ishkhanov, B. B. Lur'e St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences
Abstract:
In the present paper, the embedding problem is considered for number fields with $p$-groups whose kernel is either of two groups with two generators $\alpha$ and $\beta$ and with the following relations:
(1) $\alpha^p=1$, $\beta^p=1$, $[\alpha,\beta,\beta]=1$, $[\alpha,\beta,\alpha,\alpha]=1$ or
(2) $\alpha^p=[\alpha,\beta,\alpha]$, $\beta^p=1$, $[\alpha,\beta,\beta]=1$.
It is shown that for the solvability of the original embedding problem it is necessary and sufficient to have the solvability of the associated Abelian and local problems for all completions of the base fields. Bibliography: 7 titles.
Received: 18.06.1993
Citation:
V. V. Ishkhanov, B. B. Lur'e, “On the embedding problem with non-Abelian kernel of order $p^4$. IV”, Problems in the theory of representations of algebras and groups. Part 3, Zap. Nauchn. Sem. POMI, 211, Nauka, St. Petersburg, 1994, 120–126; J. Math. Sci., 83:5 (1997), 637–641
Linking options:
https://www.mathnet.ru/eng/znsl5882 https://www.mathnet.ru/eng/znsl/v211/p120
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