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

MathSciNet review:
593449

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Abstract: Denote by the set of units of finite order of the integral group ring of a group . We determine the class of all groups such that is a subgroup and study how this property relates to certain properties of the unit groups.

**[1]**M. M. Parmenter and C. Polcino Milies,*Group rings whose units form a nilpotent or FC group*, Proc. Amer. Math. Soc.**68**(1978), no. 2, 247–248. MR**0498817**, 10.1090/S0002-9939-1978-0498817-9**[2]**Sudarshan K. Sehgal,*Topics in group rings*, Monographs and Textbooks in Pure and Applied Math., vol. 50, Marcel Dekker, Inc., New York, 1978. MR**508515****[3]**S. K. Sehgal and H. J. Zassenhaus,*Integral group rings with nilpotent unit groups*, Comm. Algebra**5**(1977), no. 2, 101–111. MR**0447321****[4]**Sudarshan K. Sehgal and Hans J. Zassenhaus,*Group rings whose units form an FC-group*, Math. Z.**153**(1977), no. 1, 29–35. MR**0435197**

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1981-0593449-6

Keywords:
Group rings,
unit groups,
torsion units,
nilpotent,
group

Article copyright:
© Copyright 1981
American Mathematical Society