Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 12F10, 12-04, 12E10, 65H10

Retrieve articles in all journals with MSC: 12F10, 12-04, 12E10, 65H10

Additional Information

PII: S 0025-5718(1988)0958642-3
Article copyright: © Copyright 1988 American Mathematical Society