Some congruences on prime factors of class number of algebraic extensions

Dissertant

Asad, Yusuf Atif M. Dabbur

Thesis advisor

Sarsour, Jasir H.

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

Mathematics

Topics

• Algebraic fields

No. of Pages

61

Table of Contents

• APA
• MLA
• AMA

Language

English

Data Type

Arab Theses

Record ID

BIM-300269