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Totally Real Subfields of p-Adic Fields having the Symmetric Group as Galois Group

Published online by Cambridge University Press:  20 November 2018

Howard Kleiman
Howard Kleiman*
Affiliation:
Queensborough Community College, Bayside, New York
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In this paper, an elementary proof is given of the following proposition:

Theorem 1. If Qp is an arbitrary field of p-adic numbers, then it contains normal subfields Ln(2 ≤ n ≤ p) which have symmetric groups Sn as their respective Galois groups over Q, the field of rational numbers. Furthermore, each Ln may be chosen to be totally real.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 3 , September 1971 , pp. 441 - 442
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Perron, O., Algebra, de Gruyter, Berlin, 2 (1951), p. 220.Google Scholar
2. Weisner, L., Irreducibility of polynomials of degree n which assume the same value n times. Bull. Amer. Math. Soc. 41 (1935), 238-252.Google Scholar