For any nonsplit p > 2-extension of finite groups with a cyclic kernel and a quotient group with two generators all the accompanying extensions of which split, there exists a realization of the quotient group as a Galois group of number fields such that the corresponding embedding problem is ultrasolvable (i.e., this embedding problem is solvable and has only fields as solutions).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 452, 2016, pp. 132–157.
Translated by N. B. Lebedinskaya.
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Kiselev, D.D., Chubarov, I.A. On the Ultrasolvability of Some Classes of Minimal Nonsplit p-Extensions with Cyclic Kernel for p > 2. J Math Sci 232, 677–692 (2018). https://doi.org/10.1007/s10958-018-3897-7
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DOI: https://doi.org/10.1007/s10958-018-3897-7