Lie properties of symmetric elements in group rings II

Let F be a field of characteristic different from 2, and G a group with involution *. Write (F G)+ for the set of elements in the group ring F G that are symmetric with respect to the induced involution. Recently, Giambruno, Polcino Milies and Sehgal showed that if G has no 2-elements, and (F G)+ is Lie nilpotent (resp. Lie n-Engel), then F G is Lie nilpotent (resp. Lie m-Engel, for some m). Here, we classify the groups containing 2-elements such that (F G)+ is Lie nilpotent or Lie n-Engel. © 2008 Elsevier B.V. All rights reserved.