Kiselev, D. D. On ultrasolvable embedding problems with cyclic kernel. (English) Zbl 1420.12002 Russ. Math. Surv. 71, No. 6, 1149-1151 (2016); translation from Usp. Mat. Nauk 71, No. 6, 165-166 (2016). Continuing studies of Ishkanov, Lur’e and the author himself, the following is proved. Theorem 1. There is an infinite sries of examples of ultrasolvable embedding problems over number fields with cyclic kernels of order \(n\). Theorem 2. Let \(k\in\mathbb Q(\varepsilon _n)\) be given. For each prime \(p\mid n\) put \(K_p = k(\sqrt[p^2]{\tilde u_p})\), where \(\tilde u_p\in k^+\) (see Lemma 2). Put \(K =\otimes_{p\mid n}K_p\). Then there exists an ultrasolvable embedding problem of the extension \(K/k\) with cyclic kernel of order \(n\). The necessary requirements for their proofs are provided in Lemmas 1–3. Reviewer: Olaf Ninnemann (Uffing am Staffelsee) Cited in 2 Documents MSC: 12F10 Separable extensions, Galois theory PDF BibTeX XML Cite \textit{D. D. Kiselev}, Russ. Math. Surv. 71, No. 6, 1149--1151 (2016; Zbl 1420.12002); translation from Usp. Mat. Nauk 71, No. 6, 165--166 (2016) Full Text: DOI DOI