Lie properties of the group algebra and the nilpotency class of the group of units

DOI10.1006/jabr.1998.7617zbMath0936.16028OpenAlexW2059802592WikidataQ115395841 ScholiaQ115395841MaRDI QIDQ1284097

Adalbert Bovdi, János Kurdics

Publication date: 11 May 2000

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

Full work available at URL: https://doi.org/10.1006/jabr.1998.7617

zbMATH Keywords

group algebrasfinite \(p\)-groupsnilpotent groupsSylow subgroupsgroup of unitsmodular group algebrasmetabelian groupsnilpotency classesLie nilpotency indices

Mathematics Subject Classification ID

Group rings (16S34) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Finite nilpotent groups, (p)-groups (20D15) Derived series, central series, and generalizations for groups (20F14) Units, groups of units (associative rings and algebras) (16U60)

Related Items

Group algebras with almost maximal Lie nilpotency index., Lie nilpotency indices of modular group algebras II, Modular group algebras with almost maximal Lie nilpotency indices., On the Lie nilpotency indices of modular group algebras, Group algebras of Lie nilpotency index 12 and 13, Lie Dimension Subgroups and Central Series Related to Group Algebras, Group of units of finite group algebras for groups of order 24, The unit groups of semisimple group algebras of some non-metabelian groups of order $144$, Unnamed Item, Nilpotency Indices of Symmetric Elements of Group Algebras, Lie structure of smash products, Lie nilpotency index of a modular group algebra, On Lie nilpotent modular group algebras, Lie Nilpotency Indices of Restricted Universal Enveloping Algebras, Units in finite dihedral and quaternion group algebras., On unit group of finite semisimple group algebras of non-metabelian groups of order 108, A note on Lie nilpotent group algebras, Group algebras of Lie nilpotency index 14, Lie Nilpotency Indices of Modular Group Algebras, A note on the upper Lie nilpotency index of a group algebra, Lie Nilpotent Group Algebras and Upper Lie Codimension Subgroups, On the order of unitary subgroup of the modular group algebra 𝔽_2^kD_2N, On the lower Lie nilpotency index of a group algebra, Strongly Lie nilpotent group algebras of index at most 8

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