The Theory of Finite Groups
An Introduction
Seiten
2003
Springer-Verlag New York Inc.
978-0-387-40510-0 (ISBN)
Springer-Verlag New York Inc.
978-0-387-40510-0 (ISBN)
From reviews of the German edition:
"This is an exciting text and a refreshing contribution to an area in which challenges continue to flourish and to captivate the viewer.
From reviews of the German edition:
"This is an exciting text and a refreshing contribution to an area in which challenges continue to flourish and to captivate the viewer. Even though representation theory and constructions of simple groups have been omitted, the text serves as a springboard for deeper study in many directions. One who completes this text not only gains an appreciation of both the depth and the breadth of the theory of finite groups, but also witnesses the evolutionary development of concepts that form a basis for current investigations. This is accomplished by providing a thread that permits a natural flow from one concept to another rather than compartmentalizing. Operators on sets and groups are introduced early and used effectively throughout. The bibliography provides excellent supplemental support...The text is tight; there is no fluff. The format builds on concepts essential for later expansion and associated reading. On occasion, results are stated without proof; continuity is maintained. Several proofs are provided free of representation theory on which the originals were based. More generally the proofs are direct, perhaps at times brief. The focus is on the underlying structural components, with selected details left to the reader. As a result the reader develops the maturity required for approaching the literature with confidence. The first eight chapters have an abundance of exercises, not prorated, and some of the more challenging are addressed later in the text. Due to the nature of the material, fewer exercises appear in the remaining chapters." (H. Bechtell, Mathematical Reviews)
"This is an exciting text and a refreshing contribution to an area in which challenges continue to flourish and to captivate the viewer.
From reviews of the German edition:
"This is an exciting text and a refreshing contribution to an area in which challenges continue to flourish and to captivate the viewer. Even though representation theory and constructions of simple groups have been omitted, the text serves as a springboard for deeper study in many directions. One who completes this text not only gains an appreciation of both the depth and the breadth of the theory of finite groups, but also witnesses the evolutionary development of concepts that form a basis for current investigations. This is accomplished by providing a thread that permits a natural flow from one concept to another rather than compartmentalizing. Operators on sets and groups are introduced early and used effectively throughout. The bibliography provides excellent supplemental support...The text is tight; there is no fluff. The format builds on concepts essential for later expansion and associated reading. On occasion, results are stated without proof; continuity is maintained. Several proofs are provided free of representation theory on which the originals were based. More generally the proofs are direct, perhaps at times brief. The focus is on the underlying structural components, with selected details left to the reader. As a result the reader develops the maturity required for approaching the literature with confidence. The first eight chapters have an abundance of exercises, not prorated, and some of the more challenging are addressed later in the text. Due to the nature of the material, fewer exercises appear in the remaining chapters." (H. Bechtell, Mathematical Reviews)
Basic Concepts.- Abelian Groups.- Action and Conjugation.- Permutation Groups.- p-Groups and Nilpotent Groups.- Normal and Subnormal Structure.- Transfer and p-Factor Groups.- Groups Acting on Groups.- Quadratic Action.- The Embedding of p-Local Subgroups.- Signalizer Functors.- N-Groups.
| Reihe/Serie | Universitext |
|---|---|
| Zusatzinfo | XII, 388 p. |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 0-387-40510-0 / 0387405100 |
| ISBN-13 | 978-0-387-40510-0 / 9780387405100 |
| Zustand | Neuware |
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Buch | Softcover (2022)
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