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Group Rings with Units of Bounded Exponent over the Center
Published online by Cambridge University Press: 20 November 2018
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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.
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- 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
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
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