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Embedding covers and the theory of frobenius fields

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Abstract

We show that the theory of Frobenius fields is decidable. This is conjectured in [4], [8] and [13], and we prove it by solving a group theoretic problem to which this question is reduced there. To do this we present and develop the notion of embedding covers of finite and pro-finite groups. We also answer two other problems from [8], again by solving a corresponding group theoretic problem: A finite extension of a Frobenius field need not be Frobenius and there are PAC fields which are not Frobenius fields.

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Authors and Affiliations

  1. Tel Aviv University, Tel Aviv, Israel

    Dan Haran & Alexander Lubotzky

  2. Bar Ilan University, Ramat Gan, Israel

    Dan Haran & Alexander Lubotzky

Authors
  1. Dan Haran
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  2. Alexander Lubotzky
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Portions of this work will be incorporated in the doctoral dissertation of the first author done in Tel Aviv University under the supervision of Prof. Moshe Jarden.

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Haran, D., Lubotzky, A. Embedding covers and the theory of frobenius fields. Israel J. Math. 41, 181–202 (1982). https://doi.org/10.1007/BF02771720

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  • DOI: https://doi.org/10.1007/BF02771720

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