Hostname: page-component-77c89778f8-rkxrd Total loading time: 0 Render date: 2024-07-24T22:57:22.705Z Has data issue: false hasContentIssue false

Twisted Group Rings Whose Units Form an FC-Group

Published online by Cambridge University Press:  20 November 2018

Victor Bovdi*
Affiliation:
Department of Mathematics Bessenyei Teachers ' Training CollegeNyíregyháza, Hungary
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let U(KλG) be the group of units of the infinite twisted group algebra KλG over a field K. We describe the FC-centre ΔU of U(KλG) and give a characterization of the groups G and fields K for which U(KλG) = ΔU. In the case of group algebras we obtain the Cliff-Sehgal-Zassenhaus theorem.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1995

References

Sehgal, S.K. and Zassenhaus, H.J., Group rings whose units form an FC-group, Math. Z. 153(1977), 2935.Google Scholar
Cliff, H. and Sehgal, S.K., Group rings whose units form an YC-group, Math. Z. 161(1978), 169183.Google Scholar
Neumann, B.H., Groups with finite clasess of conjugate elements, Proc. London Math. Soc. 1(1951), 178187.Google Scholar
Kertész, A., Lectures on artinian rings, Akadémiai Kiadó, Budapest, 1987.Google Scholar
Bovdi, A.A., Group rings, Kiev, UMK VO, 1988.Google Scholar
Passman, D.S., The algebraic structure of group rings, John Wiley & Sons, New York, Sydney, Toronto, 1977.Google Scholar
Scott, W.R., On the multiplicative group of a division ring, Proc. Amer. Math. Soc. 8(1957), 303305.Google Scholar
Fuchs, L., Abelian groups, Budapest, Publishing House of Hungar. Acad. Sci., 1959.Google Scholar
Kurosh, A.G., Theory of Groups, New York, Chelsea, 1955.Google Scholar
Richardson, J.S., Primitive idempotents and the socle in group rings of periodic abelian groups, Compositio Math. 32(1976), 203223.Google Scholar