Ultrasolvable and Sylow extensions with cyclic kernel
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D. D. Kiselev and A. V. Yakovlev
Translated by: A. V. Yakovlev - St. Petersburg Math. J. 30 (2019), 95-102
- DOI: https://doi.org/10.1090/spmj/1531
- Published electronically: December 5, 2018
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Abstract:
An extension of finite groups is said to be ultrasolvable if there exists a Galois extension of number fields such that its Galois group is a factor group of this group extension and all solutions of the corresponding embedding problem are fields. In the paper, necessary and sufficient conditions of the ultrasolvability of a group extension are obtained for extensions of odd order with cyclic kernel.References
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Bibliographic Information
- D. D. Kiselev
- Affiliation: All-Russian Academy of Foreign Trade, the Ministry of Economic Development of RF, ul. Pudovkina 4a, 119285 Moscow, Russia
- Email: denmexmath@yandex.ru
- A. V. Yakovlev
- Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetsky prospekt 28, Peterhof, St. Petersburg 198504, Russia
- Email: yakovlev.anatoly@gmail.com
- Received by editor(s): October 25, 2017
- Published electronically: December 5, 2018
- © Copyright 2018 American Mathematical Society
- Journal: St. Petersburg Math. J. 30 (2019), 95-102
- MSC (2010): Primary 12F10; Secondary 12F12, 11R32
- DOI: https://doi.org/10.1090/spmj/1531
- MathSciNet review: 3790746