This book is based on a course given by the author at Harvard University in the fall semester of 1988. The course focused on the inverse problem of Galois Theory: the construction of field extensions having a given finite group as Galois group. In the first part of the book, classical methods and results, such as the Scholz and Reichardt construction for p-groups, p not equal 2, as well as Hilbert s irreducibility theorem and the large sieve inequality, are presented. The second half is devoted to rationality and rigidity criteria and their application in realizing certain groups as Galois groups of regular extensions of Q(T). While proofs are not carried out in full detail, the book contains a number of examples, exercises, and open problems.
Topics in Galois Theory (Research Notes in Mathematics): 1
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This is a very stimulating text, which . . . will attract mathematicians working in group theory, number theory, algebraic geometry, and complex analysis. --Zentralblatt für Mathematik, Review of First Edition
This small book contains a nice introduction to some classical highlights and some recent work on the inverse Galois theory problem. The topics and main theorems are carefully chosen and composed in a masterly manner. --Mathematical Reviews, Review of First Edition
This small book contains a nice introduction to some classical highlights and some recent work on the inverse Galois theory problem. The topics and main theorems are carefully chosen and composed in a masterly manner. --Mathematical Reviews, Review of First Edition
About the Author
Jean-Pierre Serre is one of the leading mathematicians of the twentieth century, active in algebraic geometry, number theory, and topology. He has received numerous awards and honors for his mathematical research and exposition, including the Fields Medal in 1954 and the Abel Prize in 2003.
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Key Phrases - Statistically Improbable Phrases (SIPs):
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weak approximation property, sieve inequality, algebraic fundamental group, irreducibility theorem, rigidity method, ramification type, inertia group, conjugacy classes, cyclic extension, regular extension, embedding problem, maximal subgroups, alternating group Key Phrases - Capitalized Phrases (CAPs): (learn more)
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weak approximation property, sieve inequality, algebraic fundamental group, irreducibility theorem, rigidity method, ramification type, inertia group, conjugacy classes, cyclic extension, regular extension, embedding problem, maximal subgroups, alternating group Key Phrases - Capitalized Phrases (CAPs): (learn more)
The Frattini, Proof of Shih Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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