Introduction to the Galois Correspondence

Introduction to the Galois Correspondence by Maureen H. Fenrick.

In this presentation of the Galois correspondence, modem theories of groups and fields are used to study problems, some of which date back to the ancient Greeks. The techniques used to solve these problems, rather than the solutions themselves, are of primary importance. The ancient Greeks were conc...

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Bibliographic Details
Main Author: Fenrick, Maureen H. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 1992.
Edition:1st ed. 1992.
Series:Springer eBook Collection.
Subjects:
Group theory.
Algebra.
Field theory (Physics).
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • I. Preliminaries - Groups and Rings
  • 1. Introduction to Groups
  • 2. Quotient Groups and Sylow Subgroups
  • 3. Finite Abelian Groups and Solvable Groups
  • 4. Introduction to Rings
  • 5. Factoring in F[x]
  • II. Field Extensions
  • 1. Simple Extensions
  • 2. Algebraic Extensions
  • 3. Splitting Fields and Normal Extensions
  • III. The Galois Correspondence
  • 1. The Fundamental Correspondence
  • 2. The Solvable Correspondence
  • IV. Applications
  • 1. Constructibility
  • 2. Roots of Unity
  • 3. Wedderburn’s Theorem
  • 3. Dirichlet’s Theorem and Finite Abelian Groups.

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