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Twisted group rings whose units form an FC-group

By Victor Bovdi


Abstract. Let U(KλG) be the group of units of an infinite twisted group algebra KλG over a field K. We describe the maximal FC-subgroup of U(KλG) and give a characterization of U(KλG) with finitely conjugacy classes. In the case of group algebras we obtain the Cliff-Sehgal-Zassenhaus ’ theorem. 1. Introduction. Let G be a group, K a field and λ: G×G ↦− → U(K) a 2-cocycle of G with respect to the trivial action G. Then the twisted group algebra KλG of G over field K is an associative K-algebra with basis {ug | g ∈ G} and with multiplication defined for all g, h ∈ G uguh = λg,hugh, (λg,h ∈ λ

Year: 1995
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