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Mathematics of Computation

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Polynomials with Galois groups $ {\rm Aut}(M\sb {22}),\;M\sb {22},$ and $ {\rm PSL}\sb 3({\bf F}\sb 4)\cdot 2\sb 2$ over $ {\bf Q}$

Author: Gunter Malle
Journal: Math. Comp. 51 (1988), 761-768
MSC: Primary 12F10; Secondary 12-04, 12E10, 65H10
MathSciNet review: 958642
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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.

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Article copyright: © Copyright 1988 American Mathematical Society

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