Nonsolvable nonic number fields ramified only at one small prime
نویسندگان
چکیده
منابع مشابه
The nonexistence of nonsolvable octic number fields ramified only at one small prime
We prove that there is no primitive octic number field ramified only at one small prime, and so no such number field with a nonsolvable Galois group.
متن کاملNonsolvable number fields ramified only at 3 and 5
For p = 3 and p = 5, we exhibit a finite nonsolvable extension of Q which is ramified only at p via explicit computations with Hilbert modular forms. The study of Galois number fields with prescribed ramification remains a central question in number theory. Class field theory, a triumph of early twentieth century algebraic number theory, provides a satisfactory way to understand solvable extens...
متن کاملNumber Fields Ramified at One Prime
For G a finite group and p a prime, a G-p field is a Galois number field K with Gal(K/Q) ∼= G and disc(K) = ±p for some a. We study the existence of G-p fields for fixed G and varying p. For G a finite group and p a prime, we define a G-p field to be a Galois number field K ⊂ C satisfying Gal(K/Q) ∼= G and disc(K) = ±p for some a. Let KG,p denote the finite, and often empty, set of G-p fields. ...
متن کاملNonsolvable Groups Satisfying the One-Prime Hypothesis
Throughout this paper, G is a finite group and Irr(G) is the set of irreducible characters of G. We are particularly interested in the values these characters take on the identity of G. If χ ∈ Irr(G), then χ(1) is the degree of χ. The set of all degrees for G is written cd(G) = {χ(1) |χ ∈ Irr(G)}. In recent years, there has been much interest in finding connections between the structure of a fi...
متن کاملNonic 3-adic Fields
We compute all nonic extensions of Q3 and find that there are 795 of them up to isomorphism. We describe how to compute the associated Galois group of such a field, and also the slopes measuring wild ramification. We present summarizing tables and a sample application to number fields.
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: Journal de Théorie des Nombres de Bordeaux
سال: 2006
ISSN: 1246-7405
DOI: 10.5802/jtnb.562