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The leading coefficient of units

  • Klaus W. Roggenkamp
  • Martin J. Taylor
Part of the DMV Seminar book series (OWS, volume 18)

Abstract

The aim in this section is to prove the following

III.1. Theorem. (Saksonov)[Sak; 71]. Let G be a finite group and R an integral domain of characteristic zero, in which no rational prime divisor of |G| is invertible.

If uV(RG) is a unit of finite order n, then n is a divisor of |G| and either u(1) = 0 or u = u(1), where u(1) is the coefficient of1 in {Equ1 page 15}

In particular, if u ∈ V(RG) is a non trivial unit of finite order, then u(1) = 0.

Keywords

Characteristic Zero Group Ring Finite Order Splitting Field Isomorphism Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 1992

Authors and Affiliations

  • Klaus W. Roggenkamp
    • 1
  • Martin J. Taylor
    • 2
  1. 1.Mathematisches Institut BUniversität StuttgartStuttgart 80Germany
  2. 2.Dept. of Mathematics U.M.I.S.T.ManchesterEngland

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