JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (8): 1-5.doi: 10.6040/j.issn.1671-9352.0.2022.555

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

Xian LING(),Jinke HAI*()   

  1. College of Mathematics and Statistics, Qingdao University, Qingdao 266071, Shandong, China
  • Received:2022-10-31 Online:2023-08-20 Published:2023-07-28
  • Contact: Jinke HAI E-mail:Z13142179243@163.com;haijinke2002@aliyun.com

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Abstract:

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.

Key words: integral group ring, torsion unit, partial augmentation, Zassenhaus?s conjecture

CLC Number: 

  • O152.6
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