![](/images/graphics-bg.png)
Some congruences on prime factors of class number of algebraic extensions
Dissertant
Thesis advisor
University
Islamic University
Faculty
Faculty of Science
Department
Department of Mathematics
University Country
Palestine (Gaza Strip)
Degree
Master
Degree Date
2010
English Abstract
In this thesis, we study some congruence's on the odd prime factors of the class number of the number fields.
We say that a finite Galois extension L / K is Galois solvable if the Galois group Gal (L / K) is solvable. The main result studied is : Let L / Q be a finite algebraic extension with [L : Q] = 2α0 × N1, where N1 > 1 is odd. Suppose that there exists a field K ⊂ L with [K : Q] = 2α0 and with L / K Galois solvable extension.
Let h (L) is the class number of L.
Suppose that h (L) > 1.
Let p be a prime dividing h (L).
Let rp be the rank of the p−class group of L.
If p хII rp i = 1(pi-1) and N1 are cop rime, then p divides the class number h (K) of K.
Main Subjects
Topics
No. of Pages
61
Table of Contents
Abstract.
Contents.
Chapter 1 : Preliminaries.
Chapter 2 : Number fields and rings of algebraic integers.
Chapter 3 : Factorization of ideals and the class number.
Chapter 4 : Some congruences on prime factors of class number of finite algebraic extensions K / Q.
American Psychological Association (APA)
Asad, Yusuf Atif M. Dabbur. (2010). Some congruences on prime factors of class number of algebraic extensions. (Master's theses Theses and Dissertations Master). Islamic University, Palestine (Gaza Strip)
https://search.emarefa.net/detail/BIM-300269
Modern Language Association (MLA)
Asad, Yusuf Atif M. Dabbur. Some congruences on prime factors of class number of algebraic extensions. (Master's theses Theses and Dissertations Master). Islamic University. (2010).
https://search.emarefa.net/detail/BIM-300269
American Medical Association (AMA)
Asad, Yusuf Atif M. Dabbur. (2010). Some congruences on prime factors of class number of algebraic extensions. (Master's theses Theses and Dissertations Master). Islamic University, Palestine (Gaza Strip)
https://search.emarefa.net/detail/BIM-300269
Language
English
Data Type
Arab Theses
Record ID
BIM-300269