Profinite Groups
Seiten
1998
Oxford University Press (Verlag)
978-0-19-850082-7 (ISBN)
Oxford University Press (Verlag)
978-0-19-850082-7 (ISBN)
Profinite groups are of interest to mathematicians in a variety of areas, including number theory, abstract groups, and analysis. This text provides an introduction to the subject and is designed to convey basic facts and enable readers to enhance their skills in manipulating profinite groups.
This is the first book to be dedicated entirely to profinite groups, an area of algebra with important links to number theory and other areas of mathematics. It provides a comprehensive overview of the subject; prerequisite knowledge is kept to a minimum, and several major theorems are presented in an accessible form. The book would provide a valuable introduction for postgraduate students, or form a useful reference for researchers in other areas. The first few chapters lay the foundations and explain the role of profinite groups in number theory. Later chapters explore various aspects of profinite groups in more detail; these contain accessible and lucid accounts of many major theorems. Prerequisites are kept to a minimum with the basic topological theory summarized in an introductory chapter.
This is the first book to be dedicated entirely to profinite groups, an area of algebra with important links to number theory and other areas of mathematics. It provides a comprehensive overview of the subject; prerequisite knowledge is kept to a minimum, and several major theorems are presented in an accessible form. The book would provide a valuable introduction for postgraduate students, or form a useful reference for researchers in other areas. The first few chapters lay the foundations and explain the role of profinite groups in number theory. Later chapters explore various aspects of profinite groups in more detail; these contain accessible and lucid accounts of many major theorems. Prerequisites are kept to a minimum with the basic topological theory summarized in an introductory chapter.
0. Topological preliminaries ; 1. Profinite groups and completions ; 2. Sylow theory ; 3. Galois theory ; 4. Finitely generated groups and countably based groups ; 5. Free groups and projective groups ; 6. Modules, extensions, and duality ; 7. Modules for completed group algebras ; 8. Profinite groups of finite rank ; 9. Cohomology of profinite groups ; 10. Further cohomological methods ; 11. Groups of finite cohomological dimension ; 12. Finitely presented pro-p groups
| Erscheint lt. Verlag | 1.10.1998 |
|---|---|
| Reihe/Serie | London Mathematical Society Monographs ; 19 |
| Zusatzinfo | line figures |
| Verlagsort | Oxford |
| Sprache | englisch |
| Maße | 161 x 242 mm |
| Gewicht | 588 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie |
| ISBN-10 | 0-19-850082-3 / 0198500823 |
| ISBN-13 | 978-0-19-850082-7 / 9780198500827 |
| Zustand | Neuware |
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