The derived length of Lie soluble group rings. I

DOI10.1016/0022-4049(92)90111-RzbMath0765.16007WikidataQ115364427 ScholiaQ115364427MaRDI QIDQ1196782

Aner Shalev

Publication date: 16 January 1993

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

zbMATH Keywords

group algebrasLie algebrasderived lengthscommutator subgroupLie soluble group 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 (13)

Derived lengths of symmetric Poisson algebras ⋮ Lie identities for Hopf algebras ⋮ Restricted enveloping algebras with minimal Lie derived length ⋮ Lie solvable enveloping algebras of characteristic two ⋮ Lie derived length and involutions in group algebras. ⋮ Lie centre-by-metabelian group algebras in even characteristic. I ⋮ Group algebras with minimal Lie derived length. ⋮ GROUP ALGEBRAS WHICH ARE LIE SOLVABLE OF DERIVED LENGTH THREE ⋮ Lie structure of smash products ⋮ On the derived length of the unit group of a group algebra ⋮ Lie Derived Lengths of Group Algebras of Groups with Cyclic Derived Subgroup ⋮ COMMUTATOR IDENTITIES ON SYMMETRIC ELEMENTS OF GROUP ALGEBRAS ⋮ Solvable symmetric Poisson algebras and their derived lengths

Cites Work

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• Lie ideals in group rings
• Dimension subgroups, nilpotency indices, and the number of generators of ideals in p-group algebras
• On Lie nilpotent group rings
• The Baer condition for group algebras
• Lie centrally metabelian group rings
• Lie Dimension Subgroups, Lie Nilpotency Indices, and the Exponent of the Group of Normalized Units
• Lie-Nilpotency Indices of Group Algebras
• The Derived Length of Lie Soluble Group Rings II
• Lie Solvable Group Rings
• The Structure of the Group Ring of a p-Group Over a Modular Field

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