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Integral Group Rings with Nilpotent Unit Groups

Published online by Cambridge University Press:  20 November 2018

César Polcino Milies
César Polcino Milies*
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, Brasil
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Let R be a ring with unit element and G a finite group. We denote by RG the group ring of the group G over R and by U(RG) the group of units of this group ring.

The study of the nilpotency of U(RG) has been the subject of several papers.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 5 , 01 October 1976 , pp. 954 - 960
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Bateman, J. M. and Coleman, D. B., Group algebras with nilpotent unit groups, Proc. Amer. Math. Soc. 19 (1968), 448–449.Google Scholar
2. Berman, S. D., On the equation xm — 1 in an integral group ring, Ukrain. Mat. Z 7 (1955), 253–261.Google Scholar
3. Bovdi, A. A., The periodic normal divisors of the multiplicative group of a group ring II, Sibirsk. Mat. 1 11 (1970), 492–511.Google Scholar
4. Higman, G., The units of group rings, Proc. London Math. Soc. Jfi (1940), 231–248.Google Scholar
5. Khripta, I. I., The nilpotency of the multiplicative group of a group ring, Mat. Zametki 11 (1972), 191–200.Google Scholar
6. Motose, K. and Tominaga, H., Group rings with nilpotent unit groups, Math. J. Okayama Univ. U (1969), 43–46.Google Scholar
7. Polcino Milies, C., The nilpotency of the group of units of a group ring, Atas da 3a. Escola de Algebra, 1974, to appear.Google Scholar
8. Raggi, F. F. Cardenas, Las unidades en anillos de grupo con coeficientes en Kp n, Zp n y Zp, Anales Inst. Mat. Univ. Nac. Aut. Mexico 10 (1970), 29–65.Google Scholar
9. Takahashi, S., Some properties of the group ring over rational integers of a finite group, Notices Amer. Math. Soc. 12 (1965), 463.Google Scholar