Polynomials with Galois groups $\textrm {Aut}(M_ {22}),\;M_ {22},$ and $\textrm {PSL}_ 3(\textbf {F}_ 4)\cdot 2_ 2$ over $\textbf {Q}$
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- by Gunter Malle PDF
- Math. Comp. 51 (1988), 761-768 Request permission
Abstract:
In this paper the construction of infinite families of polynomials with Galois groups $\operatorname {Aut} ({M_{22}})$, ${M_{22}}$ and ${\text {PSL}_3}({\mathbb {F}_4})\;\cdot \;2$ over $\mathbb {Q}$ is achieved. The determination of these polynomials leads to a system of nonlinear algebraic equations in 22 unknowns. The solutions belonging to the Galois extensions with the desired Galois groups are computed with a p-modular version of the Buchberger algorithm. The application of this method, which is described in some detail, turns out to be feasible even for relatively large systems of nonlinear equations.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Math. Comp. 51 (1988), 761-768
- MSC: Primary 12F10; Secondary 12-04, 12E10, 65H10
- DOI: https://doi.org/10.1090/S0025-5718-1988-0958642-3
- MathSciNet review: 958642