The lien-engel property in group rings

DOI10.1080/00927870008826866zbMath0952.20006OpenAlexW2043820567MaRDI QIDQ4944398

Gregory T. Lee

Publication date: 15 January 2001

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927870008826866

zbMATH Keywords

group algebrasinvolutionsquaternion groupskew symmetric elementsLie \(n\)-Engel rings

Mathematics Subject Classification ID

Group rings (16S34) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Rings with involution; Lie, Jordan and other nonassociative structures (16W10)

Related Items (14)

Unnamed Item ⋮ Oriented group involutions in group algebras: a survey ⋮ Lie identities on symmetric elements of restricted enveloping algebras ⋮ Star group identities on units of group algebras ⋮ Anticommutativity of symmetric elements under generalized oriented involutions ⋮ The bounded Lie Engel property on torsion group algebras. ⋮ Group Rings Whose Symmetric Units Generate ann-Engel Group ⋮ LIE METABELIAN SKEW ELEMENTS IN GROUP RINGS ⋮ Lie Properties of Symmetric Elements Under Oriented Involutions ⋮ Groups whose irreducible representations have degree at most 2. ⋮ On the Lie algebra of skew-symmetric elements of an enveloping algebra ⋮ Group algebras whose symmetric and skew elements are Lie solvable ⋮ Lie properties of symmetric elements in group rings. II. ⋮ Group rings whose skew elements are bounded Lie Engel.

Cites Work

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• Symmetric units and group identities
• Lie nilpotence of group rings
• Group rings whose symmetric elements are Lie nilpotent
• Group algebras whose units satisfy a group identity. II
• Lie Solvable Group Rings

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