Nilpotent Symmetric Units in Group Rings

DOI10.1081/AGB-120017331zbMath1033.16013OpenAlexW2075131619MaRDI QIDQ4801385

Gregory T. Lee

Publication date: 7 April 2003

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

Full work available at URL: https://doi.org/10.1081/agb-120017331

zbMATH Keywords

torsion groupsinvolutionsnilpotent groupsgroup ringscommutator 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) Nilpotent groups (20F18) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Units, groups of units (associative rings and algebras) (16U60)

Related Items (9)

Group rings whose symmetric units are nilpotent ⋮ Oriented group involutions in group algebras: a survey ⋮ 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 ⋮ Commutativity of symmetric elements in group rings ⋮ COMMUTATOR IDENTITIES ON SYMMETRIC ELEMENTS OF GROUP ALGEBRAS

Cites Work

• Generalized polynomial identities
• Symmetric units and group identities
• Group identities on units of rings
• Lie nilpotence of group rings
• 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
• Symmetric units in modular group algebras
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