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- W2020180232 abstract "Let G be a transitive, solvable subgroup of S 6 . We show that there is a common formula for finding the roots of all irreducible sextic polynomials f ( x ) ∈ Q [ x ] with Gal( f ) = G . Moreover, once the roots r i are calculated, there is an explicit procedure for numbering them so that the Galois group acts via τ( r i ) = r τ( i ) for τ ∈ G ⊂ S 6 . We also demonstrate new criteria for determining the Galois group of an irreducible sextic polynomial f ( x ) ∈ Q [ x ]. The first two results generalize results of D. S. Dummit (1991, Math. Comp. 57, 387–401) for quintic polynomials." @default.
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- W2020180232 date "2000-11-01" @default.
- W2020180232 modified "2023-10-14" @default.
- W2020180232 title "General Formulas for Solving Solvable Sextic Equations" @default.
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- W2020180232 doi "https://doi.org/10.1006/jabr.2000.8428" @default.
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