Article ID Journal Published Year Pages File Type
4597468 Journal of Pure and Applied Algebra 2009 6 Pages PDF
Abstract

Let FF be a field of characteristic different from 2, and GG a group with involution ∗∗. Write (FG)+(FG)+ for the set of elements in the group ring FGFG that are symmetric with respect to the induced involution. Recently, Giambruno, Polcino Milies and Sehgal showed that if GG has no 2-elements, and (FG)+(FG)+ is Lie nilpotent (resp. Lie nn-Engel), then FGFG is Lie nilpotent (resp. Lie mm-Engel, for some mm). Here, we classify the groups containing 2-elements such that (FG)+(FG)+ is Lie nilpotent or Lie nn-Engel.

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Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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