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

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## Abstract

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 |
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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 |

URI: | https://research.sabanciuniv.edu/id/eprint/29240 |