The action of the Galois Group on the Torsion-free part of Unit Group in a Totally Complex Galois Extension over Q with Galois Group S3
نویسنده
چکیده
This is the senior thesis I worked on in University of Washington, under the supervision of Prof. Ralph Greenberg. We intended to classify the torsion-free part of the unit group of a totally complex normal extension with Galois group S3 as a Z[S3]-module. We obtained a way to recognize the module structure based on the class numbers of the field extensions. Conversely we also showed that some ratio of class numbers can only be 1 or 1/3, from this investigation.
منابع مشابه
ALGEBRAS WITH CYCLE-FINITE STRONGLY SIMPLY CONNECTED GALOIS COVERINGS
Let $A$ be a nite dimensional $k-$algebra and $R$ be a locally bounded category such that $R rightarrow R/G = A$ is a Galois covering dened by the action of a torsion-free group of automorphisms of $R$. Following [30], we provide criteria on the convex subcategories of a strongly simply connected category R in order to be a cycle- nite category and describe the module category of $A$. We p...
متن کاملDeformation of Outer Representations of Galois Group II
This paper is devoted to deformation theory of "anabelian" representations of the absolute Galois group landing in outer automorphism group of the algebraic fundamental group of a hyperbolic smooth curve defined over a number-field. In the first part of this paper, we obtained several universal deformations for Lie-algebra versions of the above representation using the Schlessinger criteria for...
متن کاملDeformation of Outer Representations of Galois Group
To a hyperbolic smooth curve defined over a number-field one naturally associates an "anabelian" representation of the absolute Galois group of the base field landing in outer automorphism group of the algebraic fundamental group. In this paper, we introduce several deformation problems for Lie-algebra versions of the above representation and show that, this way we get a richer structure than t...
متن کاملA History of Selected Topics in Categorical Algebra I: From Galois Theory to Abstract Commutators and Internal Groupoids
This paper is a chronological survey, with no proofs, of a direction in categorical algebra, which is based on categorical Galois theory and involves generalized central extensions, commutators, and internal groupoids in Barr exact Mal’tsev and more general categories. Galois theory proposes a notion of central extension, and motivates the study of internal groupoids, which is then used as an a...
متن کاملNonrigid Constructions in Galois Theory
The context for this paper is the Inverse Galois Problem. First we give an if and only if condition that a finite group is the group of a Galois regular extension of R(X) with only real branch points. It is that the group is generated by elements of order 2 (Theorem 1.1 (a)). We use previous work on the action of the complex conjugation on covers of P [FrD]. We also use Fried and Völklein [FrV]...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015