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Notes on the minimal number of ramified primes in some l-extensions of Q

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Abstract.

For a finite l-group G, let ramt(G) denote the minimal integer such that G can be realized as the Galois group of a tamely ramified extension of Q ramified only at ramt(G) finite primes. We study the upper bound of ramt(G) and give an improvement of the result of Plans. We also give the best bound of ramt(G) for all 3-groups G of order less than or equal to 35.

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Authors and Affiliations

  1. Mathematics Section, Division of Innovative Technology and Science, Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa, 920-1192, Japan

    Akito Nomura

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  1. Akito Nomura
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Correspondence to Akito Nomura.

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This research was partially supported by the Grants-in-Aid for Scientific Research (C), the Japan Society for the Promotion of Science.

Received: 14 September 2007

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Nomura, A. Notes on the minimal number of ramified primes in some l-extensions of Q. Arch. Math. 90, 501–510 (2008). https://doi.org/10.1007/s00013-008-2586-z

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  • DOI: https://doi.org/10.1007/s00013-008-2586-z

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