幂零群通过阿贝尔群扩张的整群环挠单位的有理共轭性

Rational conjugacy of torsion units in integral group rings of nilpotent-by-Abelian groups

设G是有限幂零群N通过有限阿贝尔群A的半直积,其中(|N|,|A|)=1,在这篇注记中,证明了在某些条件下G的整群环ZG的正规化挠单位与G中的某一元在有理群代数QG中共轭。

Let G be a semidirect product of a finite nilpotent group N by a finite Abelian group A with(|N|,|A|)=1,it is shown that under some conditions any normalized torsion unit of the integral group ring ZG of G is rationally conjugate to an element of G.