Group rings whose symmetric units are nilpotent

DOI10.1515/JGT.2007.050zbMath1128.16018MaRDI QIDQ5309028

Gregory T. Lee, Francisco César Polcino Milies, Sudarshan K. Sehgal

Publication date: 9 October 2007

Published in: Journal of Group Theory (Search for Journal in Brave)

zbMATH Keywords

group algebrastorsion groupsinvolutionsnilpotent groupsgroup ringscommutator identitiesunit groupsgroup identitiessymmetric unitsnilpotent units

Mathematics Subject Classification ID

Group rings (16S34) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Nil and nilpotent radicals, sets, ideals, associative rings (16N40) Other kinds of identities (generalized polynomial, rational, involution) (16R50) Nilpotent groups (20F18) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Units, groups of units (associative rings and algebras) (16U60)

Related Items (6)

Group rings whose unitary units are nilpotent. ⋮ Group Rings Whose Symmetric Units Generate ann-Engel Group ⋮ Nilpotency Indices of Symmetric Elements of Group Algebras ⋮ Nilpotency of group ring units symmetric with respect to an involution. ⋮ Group Rings Whose Symmetric Units are Solvable ⋮ Additive mappings and identities on unit groups of algebraic algebras

Cites Work

• Group algebras with symmetric units satisfying a group identity.
• Symmetric units and group identities
• Group identities on units of group algebras
• Lie nilpotence of group rings
• A note on u.p. groups
• Group algebras with units satisfying a group identity
• Group algebras with units satisfying a group identity II
• Group rings whose symmetric elements are Lie nilpotent
• Group algebras whose units satisfy a group identity
• Group algebras whose units satisfy a group identity. II
• Nilpotent Symmetric Units in Group Rings

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