Classgroups of Group Rings

Buch | Softcover

136 Seiten

1984
Cambridge University Press (Verlag)
978-0-521-27870-6 (ISBN)

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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.

1. Frölich's description of classgroups; 2. Character Action; 3. Swan modules; 4. Reduction thoery; 5. Torsion determinants; 6. The group logarithm; 7. Swan modules, classgroups of exceptional groups; 8. The Extension theorum for KoT; 9. Adams operations for classgroups.

Erscheint lt. Verlag	12.4.1984
Reihe/Serie	London Mathematical Society Lecture Note Series
Zusatzinfo	Worked examples or Exercises
Verlagsort	Cambridge
Sprache	englisch
Maße	152 x 229 mm
Gewicht	210 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
ISBN-10	0-521-27870-8 / 0521278708
ISBN-13	978-0-521-27870-6 / 9780521278706
Zustand	Neuware