Finite Groups: A Second Course on Group Theory

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World Scientific, 1999 - Mathematics - 123 pages
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The theory of groups, especially of finite groups, is one of the most delightful areas of mathematics. Its proofs often have elegance and crystalline beauty. This textbook is intended for the reader who has been exposed to about three years of serious mathematics.

The notion of a group appears widely in mathematics and even further afield in physics and chemistry, and the fundamental idea should be known to all mathematicians. In this textbook a purely algebraic approach is taken and the choice of material is based upon the notion of conjugacy. The aim is not only to cover basic material, but also to present group theory as a living, vibrant and growing discipline, by including references and discussion of some work up to the present day.

 

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Contents

Introduction and Assumed Knowledge
1
Series Soluble Groups and Nilpotent Groups
7
Immediate Consequences of Sylows Theorems
25
The SchurZassenhaus Theorem
37
Finite Soluble Groups up to 1960
51
Fusion
65
Composite Groups
81
The Later Theory of Finite Soluble Groups
89
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