The determination of Galois groups
نویسندگان
چکیده
منابع مشابه
The Determination of Galois Groups
A technique is described for the nontentative computer determination of the Galois groups of irreducible polynomials with integer coefficients. The technique for a given polynomial involves finding high-precision approximations to the roots of the polynomial, and fixing an ordering for these roots. The roots are then used to create resolvent polynomials of relatively small degree, the linear fa...
متن کاملGalois Groups as Permutation Groups
Writing f(T ) = (T − r1) · · · (T − rn), the splitting field of f(T ) over K is K(r1, . . . , rn). Each σ in the Galois group of f(T ) over K permutes the ri’s since σ fixes K and therefore f(r) = 0⇒ f(σ(r)) = 0. The automorphism σ is completely determined by its permutation of the ri’s since the ri’s generate the splitting field over K. A permutation of the ri’s can be viewed as a permutation ...
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The smallest non-abelian p-groups play a fundamental role in the theory of Galois p-extensions. We illustrate this by highlighting their role in the definition of the norm residue map in Galois cohomology. We then determine how often these groups — as well as other closely related, larger p-groups — occur as Galois groups over given base fields. We show further how the appearance of some Galois...
متن کاملGalois as Permutation Groups
Writing f(X) = (X− r1) · · · (X− rn), the splitting field of f(X) over K is K(r1, . . . , rn). Each σ in the Galois group of f(X) over K permutes the ri’s since σ fixes K and therefore f(r) = 0⇒ f(σ(r)) = 0. The automorphism σ is completely determined by its permutation of the ri’s since the ri’s generate the splitting field over K. A permutation of the ri’s can be viewed as a permutation of th...
متن کاملdetermination of maximal singularity free zones in the workspace of parallel manipulator
due to the limiting workspace of parallel manipulator and regarding to finding the trajectory planning of singularity free at workspace is difficult, so finding a best solution that can develop a technique to determine the singularity-free zones in the workspace of parallel manipulators is highly important. in this thesis a simple and new technique are presented to determine the maximal singula...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1973
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1973-0327712-4