Decomposition of primes in non-Galois extensions

Deniz Polat, Özgür (2014) Decomposition of primes in non-Galois extensions. [Thesis]

[thumbnail of ÖzgürDenizPolat_10026569.pdf] PDF

Download (504kB)


In this thesis we consider the following question: Given a finite separable non-Galois extension F/K of a global field K, how a prime P of K decomposes in the field F. In the first part, we study the Galois extension M/K where M is the Galois closure of F/K and action of Galois group G of M/K over the set of primes of F lying over a prime P in K. We obtain a one to one correspondence between the double coset space of G with respect to certain subgroups of G (depending on P and F) and the set of primes of F lying over P. Under this correspondence ramification indices and inertia degrees are explicitly determined. Then we investigate the case where G is a finite group of Lie type and F is the intermediate field corresponding to a parabolic subgroup of G. We obtain that the number of primes of F lying over an unrami ed place with given residue degree can be given as polynomials in a power of the characteristic of the variety G. This polynomials depend on the length function on the certain subgroups of the Weyl group of G.
Item Type: Thesis
Uncontrolled Keywords: Non-Galois extension. -- Global field. -- Prime. -- Galois group. -- Double coset space. -- Finite group of Lie type. -- Weyl group. -- Length function. -- Inertia degree. -- Rami cation index. -- Galois olmayan genişleme. -- Cisim. -- Asal. -- Galois grup. -- Çift koset uzayı. -- Sonlu Lie grupları. -- Weyl grup. -- Ramifikasyon derecesi. -- Kalan derecesi.
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: IC-Cataloging
Date Deposited: 31 Mar 2016 11:10
Last Modified: 26 Apr 2022 10:06

Actions (login required)

View Item
View Item