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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

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.
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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