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  3. Classgroups of Group Rings
  • Cited by 14
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    • Publisher:
      Cambridge University Press
      Publication date:
      April 2013
      April 1984
      ISBN:
      9781107325555
      9780521278706
      DOI:
      https://doi.org/10.1017/CBO9781107325555
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.21kg, 136 Pages
      • Subjects:
      Mathematics (general), Mathematics, Number Theory, Algebra
      Series:
      London Mathematical Society Lecture Note Series (91)
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    Subjects:
    Mathematics (general), Mathematics, Number Theory, Algebra
    Series:
    London Mathematical Society Lecture Note Series (91)
    Information

    Book description

    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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