Group Algebras with Locally Nilpotent Unit Groups

DOI10.1080/00927872.2014.982817zbMath1346.16035OpenAlexW2202028248MaRDI QIDQ2802208

Mojtaba Ramezan-Nassab

Publication date: 25 April 2016

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

Full work available at URL: https://doi.org/10.1080/00927872.2014.982817

zbMATH Keywords

group algebrasEngel conditionsgroups of unitslocally nilpotent groupslocally soluble groups

Mathematics Subject Classification ID

Group rings (16S34) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Generalizations of solvable and nilpotent groups (20F19) Other kinds of identities (generalized polynomial, rational, involution) (16R50) Local properties of groups (20E25) Engel conditions (20F45) Units, groups of units (associative rings and algebras) (16U60)

Related Items (10)

Group algebras whose p-elements form a subgroup ⋮ Some identities on twisted group algebras ⋮ Permutable subgroups in \(\mathrm{GL}_n (D)\) and applications to locally finite group algebras ⋮ Locally solvable unit group of crossed products ⋮ GROUP ALGEBRAS WITH ENGEL UNIT GROUPS ⋮ ON ENGEL QUASI-NORMAL SUBGROUP IN DIVISION RINGS WITH UNCOUNTABLE CENTER ⋮ GROUP ALGEBRAS WHOSE UNIT GROUP IS LOCALLY NILPOTENT ⋮ Weakly Lie Engel condition on group rings ⋮ Some algebraic algebras with Engel unit groups ⋮ Additive mappings and identities on unit groups of algebraic algebras

Cites Work

• Unnamed Item
• Group algebras of periodic groups of a solvable multiplicative group
• Group identities on units of rings
• Group identities on units of group algebras
• Group identities on units and symmetric units of group rings.
• Group algebras with units satisfying a group identity
• Group algebras with units satisfying a group identity II
• Group algebras whose units satisfy a group identity
• Right-Ordered Groups
• Group Algebras with a Solvable Group of Units^#

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