The lie n-engel property in group rings: Communications in Algebra: Vol 28, No 2

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Abstract

Let FGbe the group ring of a group Gover a field Fwhose characteristic is p≠ 2 Let ∗ denote the involution on FGwhich sends each group element to its inverse. Let (FG)⁺and (FG)^–denote, respectively, the sets of symmetric and skew elements with respect to ∗.The conditions under which the group ring is Lie n-Engel for some nare known.We show that if either (FG)⁺or (FG)^–- is Lie n-Engel, and Gis devoid of 2-elements, then FGis Lie m-Engel for some m. Furthermore, we completely classify the remaining groups for which (FG)⁺is Lie n-Engel.

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