Ultrasolvable embedding problems for number fields
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A. V. Yakovlev
Translated by: the author - St. Petersburg Math. J. 27 (2016), 1049-1051
- DOI: https://doi.org/10.1090/spmj/1435
- Published electronically: September 30, 2016
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Abstract:
It is proved that the existence of an ultrasolvable embedding problem $(K/k,\varphi )$ for finite extensions of the field of $p$-adic numbers implies the existence of an ultrasolvable embedding problem $(K/k,\varphi )$ for finite extensions of the field of rational numbers.References
- S. P. Demuškin, The group of a maximal $p$-extension of a local field, Izv. Akad. Nauk SSSR Ser. Mat. 25 (1961), 329–346 (Russian). MR 0123565
- —, On $2$-extensions of a local field, Sibirsk. Mat. Zh. 4 (1963), no. 4, 991–955. (Russian)
- D. D. Kiselev and B. B. Lur′e, Ultrasolvability and singularity in an embedding problem, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 414 (2013), no. Voprosy Teorii PredstavleniÄ Algebr i Grupp. 25, 113–126 (Russian, with English summary); English transl., J. Math. Sci. (N.Y.) 199 (2014), no. 3, 306–312. MR 3470598, DOI 10.1007/s10958-014-1858-3
Bibliographic Information
- A. V. Yakovlev
- Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskaya ul. 28, Stary Petergof, St. Petersburg 198504, Russia
- Email: yakovlev.anatoly@gmail.com
- Received by editor(s): October 1, 2015
- Published electronically: September 30, 2016
- © Copyright 2016 American Mathematical Society
- Journal: St. Petersburg Math. J. 27 (2016), 1049-1051
- MSC (2010): Primary 11S20; Secondary 11R32
- DOI: https://doi.org/10.1090/spmj/1435
- MathSciNet review: 3589231
Dedicated: Dedicated to SergeÄ Vladimirovich Vostokov on the occasion of his anniversary