Realizing Galois Fields
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.
KeywordsNormal Subgroup Galois Group Prime Divisor Prime Order Cyclic Subgroup
Unable to display preview. Download preview PDF.
- 1.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
- 2.Pierce, R. S., Permutation representations with trivial set stabilizers, Jour. of Alg . (to appear).Google Scholar