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DODECIC 3-ADIC FIELDS
Let n be an integer and p be a prime number. An important problem in number theory is to classify the degree n extensions of the p-adic numbers through their arithmetic invariants. The most difficultExpand
The first digit of the discriminant of Eisenstein polynomials as an invariant of totally ramified extensions of p-adic fields
Let K be an extension of the p-adic numbers with uniformizer π. Let φ and ψ be Eisenstein polynomials over K of degree n that generate isomorphic extensions. We show that, if the cardinality of theExpand
Galois Groups of 2-Adic Fields of Degree 12 with Automorphism Group of Order 6 and 12
Let p be a prime number and n a positive integer. In recent years, several authors have focused on classifying degree n extensions of the p-adic numbers; the most difficult cases arising when p∣n andExpand
Galois Groups of Even Sextic Polynomials
Abstract Let $f(x)=x^{6}+ax^{4}+bx^{2}+c$ be an irreducible sextic polynomial with coefficients from a field $F$ of characteristic $\neq 2$, and let $g(x)=x^{3}+ax^{2}+bx+c$. We show how to identifyExpand
Resolvents , masses , and Galois groups of irreducible quartic polynomials Chad
Let F be a eld and f(x) 2 F [x] an irreducible polynomial of degree four. An important problem in computational algebra is to determine the Galois group of f(x) as a transitive subgroup of S4 (theExpand
Subfields of Solvable Sextic Field Extensions
Let F be a field, f(x) in F[x] an irreducible polynomial of degree six, K the stem field of f, and G the Galois group of f over F. We show G is solvable if and only if K/F has either a quadratic orExpand
Degree 14 2-adic fields
We study the 590 nonisomorphic degree 14 extensions of the 2adic numbers by computing defining polynomials for each extesnsion as well as basic invariant data for each polynomial, including theExpand
ON GALOIS GROUPS OF TOTALLY AND TAMELY RAMIFIED SEXTIC EXTENSIONS OF LOCAL FIELDS
Let K be a finite extension of the p-adic numbers with p > 3 and L/K a totally ramified sextic extension. For each of the sixteen transitive subgroups G of S6, we count the number of nonisomorphicExpand
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