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Group Rings With Hypercentral Unit Groups

Published online by Cambridge University Press:  20 November 2018

David M. Riley
David M. Riley*
Affiliation:
Department of Mathematics, University of Alberta Edmonton, Alberta T6G 2G1
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Abstract

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Let KG be the group ring of a group G over a field K and let U(KG) be its group of units. If K has characteristic p > 0 and G contains p-elements, then it is proved that U(KG) is hypercentral if and only if G is nilpotent and G′ is a finite p-group.

Keywords

16A2720C07
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 2 , 01 April 1991 , pp. 425 - 434
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Bovdi, A.A. and Khripta, I.I., Generalized Lie nilpotent group rings, Math. USSR Sbornik (1)57(1987), 165–169.Google Scholar
2. Hall, M., The Theory of Groups. MacMillan, New York, 1959.Google Scholar
3. Khripta, I.I., Nilpotency of the multiplicative group of a group ring. Thesis, Uzgorod, 1971.Google Scholar
4. Passman, D.S., The algebraic structure of group rings. Robert E. Krieger Pub.,Malabar, 1985.Google Scholar
5. Robinson, D.J.S., A course in the theory of groups. Springer-Verlag, New York, 1980.Google Scholar
6. Robinson, D.J.S., Finiteness conditions and generalized soluble groups. Ergebnisse der Math. 62, 63, Springer- Verlag, New York, 1972.Google Scholar
7. Sehgal, S.K., Topics in group rings. Marcel Dekker, New York, 1978.Google Scholar
8. Tomkinson, M.J., FC-groups. Pitman Advanced Pub. Program, Boston, 1984.Google Scholar