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Group Rings with Units of Bounded Exponent over the Center

Published online by Cambridge University Press:  20 November 2018

Sônia P. Coelho
Sônia P. Coelho*
Affiliation:
Universidade de São Paulo, São Paulo, Brasil
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Let KG be the group ring of a group G over a field K, and U its group of units. Given a group H, we shall denote by ξ(H) the center of H and by T(H) the set of all its torsion elements.

The following question appears in [5, p. 231]: When is Un ⊂ ξ (U), for some n? It was considered by G. Cliff and S. K. Sehgal in [1], where G is assumed to be a solvable group. A complete answer at characteristic zero is given there. Also they obtain partial results at characteristic p ≠ 0, with certain restrictions on the exponent n.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 34 , Issue 6 , 01 December 1982 , pp. 1349 - 1364
Copyright
Copyright © Canadian Mathematical Society 1982

References

1. Cliff, G. H. and Sehgal, S. K., Group rings with torsion units over the center, Manuscripta Math. 33 (1980), 145–158.Google Scholar
2. Fuchs, L., Abelian groups (Hungary, 1960).Google Scholar
3. Herstein, I. N., Non commutative rings, MAA (1973).Google Scholar
4. Passman, D. S., The algebraic structure of group rings (Wiley-Interscience, New York, 1977).Google Scholar
5. Sehgal, S. K., Topics in group rings Pure and Applied Mathematics 50 (Dekker, New York, 1978).Google Scholar