Realizing Galois Fields

  • R. S. Pierce
Conference paper
Part of the International Centre for Mechanical Sciences book series (CISM, volume 287)


If F is an algebraic number field of degree n over Q and p is a prime, then F is p-realizable if there is a tor-sionfree abelian group A of rank n such that qA = A for all prines q i p and F is isomorphic to the quasi-endomorphism algebra of A. The question “for which F and p is F p-realizable?” was the subject of the paper by Pierce and Vinsonhaler. The results in that work were incomplete. In particular, the characterization of the fields that are p-realizable for all p was not considered. This note provides fragmentary information on that question in the case that F/Q is a Galois extension.


Normal Subgroup Galois Group Prime Divisor Prime Order Cyclic Subgroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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    Pierce, R.S. and Vinsonhaler, C. I., Realizing algebraic number fields, Honolulu Symposium on Abelian Groups, Lecture Notes in Mathematics, vol. 1006, Springer-Verlag, New York, 1983.Google Scholar
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    Pierce, R. S., Permutation representations with trivial set stabilizers, Jour. of Alg . (to appear).Google Scholar
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    Weiss, E., Algebraic Number Theory, McGraw-Hill, New York, 1963.MATHGoogle Scholar
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    Serre, J.-P., Local Fields, Graduate Texts in Mathematics, vol. 67, Springer-Verlag, New York, 1979.CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Wien 1984

Authors and Affiliations

  • R. S. Pierce
    • 1
  1. 1.University of ArizonaUSA

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