Kida, Masanari A Kummer theoretic construction of an \(S_3\)-polynomial with given quadratic subfield. (English) Zbl 1262.11094 Interdiscip. Inf. Sci. 16, No. 1, 17-20 (2010). Following the book of C. U. Jensen, A. Ledet and N. Yui [Generic polynomials. Constructive aspects of the inverse Galois problem. Cambridge: Cambridge University Press (2002; Zbl 1042.12001)], the polynomial \(g(X)= X^3+ sX+ s\in\mathbb Q(s)[X]\) is generic for the symmetric group \(S_3\). In the opinion of the author, the arithmetic of this polynomial is not easy to deduce from the expression itself. By using a computer algebra system, this short paper provides an \(S_3\)-polynomial whose arithmetic is closely related to the chosen parameters. It arises from a Kummer theory of certain algebraic tori. Reviewer: Richard Massy (Valenciennes) Cited in 1 Document MSC: 11R32 Galois theory Keywords:Kummer theory; Galois theory; algebraic tori; metacyclic groups Citations:Zbl 1042.12001 PDFBibTeX XMLCite \textit{M. Kida}, Interdiscip. Inf. Sci. 16, No. 1, 17--20 (2010; Zbl 1262.11094) Full Text: DOI