Group algebras with an Engel group of units

DOI10.1017/S1446788700013057zbMath1114.16028OpenAlexW2078178339MaRDI QIDQ5480047

Adalbert Bovdi

Publication date: 25 July 2006

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s1446788700013057

zbMATH Keywords

group algebrasgroups of unitsgroup identities\(n\)-Engel groupsbounded Engel groupsbounded Engel algebras

Mathematics Subject Classification ID

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

Related Items (7)

Torsion subgroups, solvability and the Engel condition in associative rings ⋮ Permutable subgroups in \(\mathrm{GL}_n (D)\) and applications to locally finite group algebras ⋮ 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 ⋮ Group Rings Whose Symmetric Units Generate ann-Engel Group ⋮ Some algebraic algebras with Engel unit groups

Cites Work

• On associative algebras satisfying the Engel condition
• Group identities on units of group algebras
• Nilpotency of the multiplicative group of a group ring
• ENGEL PROPERTIES OF THE MULTIPLICATIVE GROUP OF A GROUP ALGEBRA
• A note on u.p. groups
• Group Rings with Solvable n-Engel Unit Groups
• Group algebras with units satisfying a group identity II

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