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The S-Relative Pólya Groups and S-Ostrowski Quotients of Number Fields

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Abstract

Let K/F be a finite extension of number fields and S be a finite set of primes of F, including all the Archimedean ones. In this paper, using some results of González-Avilés (J Reine Angew Math 613:75–97, 2007), we generalize the notions of the relative Pólya group \({{\,\textrm{Po}\,}}(K/F)\) (Chabert in J Number Theory 203:360–375, 2019; Maarefparvar and Rajaei in J Number Theory 207:367-384, 2020) and the Ostrowski quotient \({{\,\textrm{Ost}\,}}(K/F)\) (Shahoseini et al. in Pac J Math 321(2):415–429, 2022) to their S-versions. Using this approach, we obtain generalizations of some well-known results on the S-capitulation map, including an S-version of Hilbert’s Theorem 94.

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Acknowledgements

The authors would like to thank the anonymous referee for his/her comments and suggestions, especially for pointing out a generalized version of Hilbert’s Theorem 94 presented by Gonzalez-Aviles [5, Theorem 2.7], to be compared with Theorem 2.17. The second author acknowledges the Pacific Institute for the Mathematical Sciences (PIMS), for the financial support as well as the University of Lethbridge for providing facilities to carry out this work.

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Authors and Affiliations

  1. Department of Mathematics, Tarbiat Modares University, Tehran, 14115-134, Iran

    Ehsan Shahoseini

  2. Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, AB, T1K 3M4, Canada

    Abbas Maarefparvar

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  1. Ehsan Shahoseini
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  2. Abbas Maarefparvar
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Correspondence to Abbas Maarefparvar.

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Communicated by Majid Gazor.

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Shahoseini, E., Maarefparvar, A. The S-Relative Pólya Groups and S-Ostrowski Quotients of Number Fields. Bull. Iran. Math. Soc. 50, 19 (2024). https://doi.org/10.1007/s41980-023-00858-5

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  • DOI: https://doi.org/10.1007/s41980-023-00858-5

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