COMMUTATOR IDENTITIES ON SYMMETRIC ELEMENTS OF GROUP ALGEBRAS

DOI10.1142/S0219498813500448zbMath1282.16041OpenAlexW2125631866MaRDI QIDQ2847689

Tibor Juhász, Enikő Tóth

Publication date: 11 September 2013

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219498813500448

zbMATH Keywords

group algebrasinvolutionsgroup ringsaugmentation idealssymmetric elementspolynomial identitiesderived lengthsnilpotency classesgroup identitiesLie commutatorsLie nilpotency indices

Mathematics Subject Classification ID

Group rings (16S34) Nil and nilpotent radicals, sets, ideals, associative rings (16N40) Other kinds of identities (generalized polynomial, rational, involution) (16R50) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Units, groups of units (associative rings and algebras) (16U60)

Cites Work

• Lie derived length and involutions in group algebras.
• The derived length of Lie soluble group rings. I
• Rings with involution
• Group rings satisfying a polynomial identity
• Group identities on units and symmetric units of group rings.
• Nilpotency class of symmetric units of group algebras
• Lie nilpotence of group rings
• Group Rings Whose Symmetric Units are Solvable
• Group rings whose symmetric elements are Lie nilpotent
• A NOTE ON THE DERIVED LENGTH OF THE UNIT GROUP OF A MODULAR GROUP ALGEBRA
• Nilpotent Symmetric Units in Group Rings
• Nilpotency Indices of Symmetric Elements of Group Algebras
• Group algebras whose symmetric and skew elements are Lie solvable
• ON THE DERIVED LENGTH OF THE GROUP OF UNITS OF A GROUP ALGEBRA
• Lie Derived Lengths of Group Algebras of Groups with Cyclic Derived Subgroup
• Lie Solvable Group Rings

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