Classgroups of group rings:
This book is a self-contained account of the theory of classgroups of group rings. The guiding philosophy has been to describe all the basic properties of such classgroups in terms of character functions. This point of view is due to A. Frohlich and it achieves a considerable simplification and clar...
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1984
|
| Schriftenreihe: | London Mathematical Society lecture note series
91 |
| Links: | https://doi.org/10.1017/CBO9781107325555 |
| Zusammenfassung: | This book is a self-contained account of the theory of classgroups of group rings. The guiding philosophy has been to describe all the basic properties of such classgroups in terms of character functions. This point of view is due to A. Frohlich and it achieves a considerable simplification and clarity over previous techniques. A main feature of the book is the introduction of the author's group logarithm, with numerous examples of its application. The main results dealt with are: Ullom's conjecture for Swan modules of p-groups; the self-duality theorem for rings of integers of tame extensions; the fixed-point theorem for determinants of group rings; the existence of Adams operations on classgroups. In addition, the author includes a number of calculations of classgroups of specific families of groups such as generalized dihedral groups, and quaternion and dihedral 2-groups. The work contained in this book should be readily accessible to any graduate student in pure mathematics who has taken a course in the representation theory of finite groups. It will also be of interest to number theorists and algebraic topologists. |
| Umfang: | 1 Online-Ressource (xiii, 119 Seiten) |
| ISBN: | 9781107325555 |
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| 520 | |a This book is a self-contained account of the theory of classgroups of group rings. The guiding philosophy has been to describe all the basic properties of such classgroups in terms of character functions. This point of view is due to A. Frohlich and it achieves a considerable simplification and clarity over previous techniques. A main feature of the book is the introduction of the author's group logarithm, with numerous examples of its application. The main results dealt with are: Ullom's conjecture for Swan modules of p-groups; the self-duality theorem for rings of integers of tame extensions; the fixed-point theorem for determinants of group rings; the existence of Adams operations on classgroups. In addition, the author includes a number of calculations of classgroups of specific families of groups such as generalized dihedral groups, and quaternion and dihedral 2-groups. The work contained in this book should be readily accessible to any graduate student in pure mathematics who has taken a course in the representation theory of finite groups. It will also be of interest to number theorists and algebraic topologists. | ||
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| id | ZDB-20-CTM-CR9781107325555 |
| illustrated | Not Illustrated |
| indexdate | 2025-03-03T11:58:04Z |
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| spelling | Taylor, Martin Classgroups of group rings Martin Taylor Cambridge Cambridge University Press 1984 1 Online-Ressource (xiii, 119 Seiten) txt c cr London Mathematical Society lecture note series 91 This book is a self-contained account of the theory of classgroups of group rings. The guiding philosophy has been to describe all the basic properties of such classgroups in terms of character functions. This point of view is due to A. Frohlich and it achieves a considerable simplification and clarity over previous techniques. A main feature of the book is the introduction of the author's group logarithm, with numerous examples of its application. The main results dealt with are: Ullom's conjecture for Swan modules of p-groups; the self-duality theorem for rings of integers of tame extensions; the fixed-point theorem for determinants of group rings; the existence of Adams operations on classgroups. In addition, the author includes a number of calculations of classgroups of specific families of groups such as generalized dihedral groups, and quaternion and dihedral 2-groups. The work contained in this book should be readily accessible to any graduate student in pure mathematics who has taken a course in the representation theory of finite groups. It will also be of interest to number theorists and algebraic topologists. Erscheint auch als Druck-Ausgabe 9780521278706 |
| spellingShingle | Taylor, Martin Classgroups of group rings |
| title | Classgroups of group rings |
| title_auth | Classgroups of group rings |
| title_exact_search | Classgroups of group rings |
| title_full | Classgroups of group rings Martin Taylor |
| title_fullStr | Classgroups of group rings Martin Taylor |
| title_full_unstemmed | Classgroups of group rings Martin Taylor |
| title_short | Classgroups of group rings |
| title_sort | classgroups of group rings |
| work_keys_str_mv | AT taylormartin classgroupsofgrouprings |