Some polynomials over ℚ(𝕥) and their Galois groups

Smith, Gene

doi:10.1090/S0025-5718-99-01160-6

Some polynomials over $\mathbb {Q}(t)$ and their Galois groups
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Math. Comp. 69 (2000), 775-796 Request permission

Abstract:

Examples of polynomials with Galois group over $\mathbb Q(t)$ corresponding to every transitive group through degree eight are calculated, constructively demonstrating the existence of an infinity of extensions with each Galois group over $\mathbb Q$ through degree eight. The methods used, which for the most part have not appeared in print, are briefly discussed.

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