The lie n-engel property in group rings |
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Authors: | Gregory T Lee |
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Institution: | Department of Mathematical Sciences , University of Alberta , Edmonton, Alberta, T6G 2G1, Canada |
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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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