The leading coefficient of units

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


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.


Characteristic Zero Group Ring Finite Order Splitting Field Isomorphism Problem 
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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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