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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Group rings whose torsion units form a subgroup


Author: César Polcino Milies
Journal: Proc. Amer. Math. Soc. 81 (1981), 172-174
MSC: Primary 16A26; Secondary 20C07
DOI: https://doi.org/10.1090/S0002-9939-1981-0593449-6
MathSciNet review: 593449
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Abstract: Denote by $ TU({\mathbf{Z}}G)$ the set of units of finite order of the integral group ring of a group $ G$. We determine the class of all groups $ G$ such that $ TU({\mathbf{Z}}G)$ is a subgroup and study how this property relates to certain properties of the unit groups.


References [Enhancements On Off] (What's this?)

  • [1] M. M. Paramenter and C. Polcino Milies, Group rings whose units form a nilpotent or $ FC$ group, Proc. Amer. Math. Soc. 68 (1978), 247-248. MR 0498817 (58:16854)
  • [2] S. K. Sehgal, Topics in group rings, Dekker, New York, 1978. MR 508515 (80j:16001)
  • [3] S. K. Sehgal and H. J. Zassenhaus, Integral group rings with nilpotent unit groups, Comm. Algebra 5 (1977), 101-111. MR 0447321 (56:5634)
  • [4] -, Group rings whose units form an $ FC$ group, Math. Z. 153 (1977), 29-35. MR 0435197 (55:8158)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0593449-6
Keywords: Group rings, unit groups, torsion units, nilpotent, $ FC$ group
Article copyright: © Copyright 1981 American Mathematical Society

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