Geodesic
Totally Real Subfields of p-Adic Fields having the Symmetric Group as Galois Group
Canadian mathematical bulletin, Tome 14 (1971) no. 3, pp. 441-442

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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. 
Kleiman, Howard. Totally Real Subfields of p-Adic Fields having the Symmetric Group as Galois Group. Canadian mathematical bulletin, Tome 14 (1971) no. 3, pp. 441-442. doi: 10.4153/CMB-1971-077-2
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[1] 1. Perron, O., Algebra, de Gruyter, Berlin, 2 (1951), p. 220. Google Scholar

[2] 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

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