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Group rings whose symmetric elements are Lie nilpotent

Authors:	Gregory T. Lee

Affiliation:	Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1

Abstract:	Let be the group ring of a group over a field , with characteristic different from . Let denote the natural involution on sending each group element to its inverse. Denote by $(FG)^{+}$ the set of symmetric elements with respect to this involution. A paper of Giambruno and Sehgal showed that provided has no -elements, if $(FG)^{+}$ is Lie nilpotent, then so is . In this paper, we determine when $(FG)^{+}$ is Lie nilpotent, if does contain -elements.

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