Dihedral Galois groups of even degree polynomials
نویسندگان
چکیده
منابع مشابه
Galois Groups of p-Adic Polynomials of Fixed Degree
Given an integer n and a group G we estimate the probability that a random, monic, degree n, p-adic polynomial has Galois group isomorphic to G. A comparison is made with classic results concerning Galois groups of random, monic, degree n polynomials with integer coefficients. We conclude by analyzing the probability that a random, monic, degree n polynomial in Z[x] has these properties: its Ga...
متن کاملGalois groups of prime degree polynomials with nonreal roots
In the process of computing the Galois group of a prime degree polynomial f(x) over Q we suggest a preliminary checking for the existence of non-real roots. If f(x) has non-real roots, then combining a 1871 result of Jordan and the classification of transitive groups of prime degree which follows from CFSG we get that the Galois group of f(x) contains Ap or is one of a short list. Let f(x) ∈ Q[...
متن کاملPolynomials Associated with Dihedral Groups
Abstract. There is a commutative algebra of differential-difference operators, with two parameters, associated to any dihedral group with an even number of reflections. The intertwining operator relates this algebra to the algebra of partial derivatives. This paper presents an explicit form of the action of the intertwining operator on polynomials by use of harmonic and Jacobi polynomials. The ...
متن کاملGalois groups of multivariate Tutte polynomials
The multivariate Tutte polynomial ẐM of a matroid M is a generalization of the standard two-variable version, obtained by assigning a separate variable ve to each element e of the ground set E. It encodes the full structure of M . Let v = {ve}e∈E , let K be an arbitrary field, and suppose M is connected. We show that ẐM is irreducible over K(v), and give three self-contained proofs that the Gal...
متن کاملComputing Galois Groups with Generic Resolvent Polynomials
Given an arbitrary irreducible polynomial f with rational coefficients it is difficult to determine the Galois group of the splitting field of that polynomial. When the roots of f are easy to calculate, there are a number of “tricks” that can be employed to calculate this Galois group. If the roots of f are solvable by radicals, for example, it is often easy to calculate by hand the Q-fixing au...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2007
ISSN: 0030-8730
DOI: 10.2140/pjm.2007.229.185