Group identities on units of group algebras

DOI10.1006/jabr.1999.8203zbMath0958.16033OpenAlexW1976656516MaRDI QIDQ1975920

Antonio Giambruno, Sudarshan K. Sehgal, Angela Valenti

Publication date: 18 January 2001

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

Full work available at URL: https://doi.org/10.1006/jabr.1999.8203

zbMATH Keywords

group algebrasnormal subgroupsnilpotent groupsunit groupsgroup identities\(p\)-elementsgroups of bounded exponent

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Periodic groups; locally finite groups (20F50) Group rings (16S34) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Nilpotent groups (20F18) Units, groups of units (associative rings and algebras) (16U60)

Related Items (26)

Group algebras whose p-elements form a subgroup ⋮ Group algebras with symmetric units satisfying a group identity. ⋮ Notes on the history of identities on group (and loop) algebras ⋮ Group and polynomial identities in group rings ⋮ ON NIL SUBSEMIGROUPS OF RINGS WITH GROUP IDENTITIES ⋮ Unnamed Item ⋮ Group rings whose symmetric units are nilpotent ⋮ Oriented group involutions in group algebras: a survey ⋮ Star-group identities and groups of units. ⋮ Group rings whose unitary units are nilpotent. ⋮ Star group identities on units of group algebras ⋮ Star-group identities on units of group algebras: the non-torsion case ⋮ Products of unipotent elements in certain algebras ⋮ GROUP ALGEBRAS WITH ENGEL UNIT GROUPS ⋮ Group Rings Whose Symmetric Units Generate ann-Engel Group ⋮ Group Algebras with a Solvable Group of Units^# ⋮ A Survey on *-Group Identities on Units of Group Rings ⋮ On group identities for the unit group of algebras and semigroup algebras over an infinite field. ⋮ POLYNOMIAL AND GROUP IDENTITIES IN ALTERNATIVE LOOP ALGEBRAS ⋮ Group Algebras with Locally Nilpotent Unit Groups ⋮ Algebras whose units satisfy a \(*\)-Laurent polynomial identity ⋮ Group Rings Whose Symmetric Units are Solvable ⋮ Identities of Group Algebras ⋮ Group algebras with an Engel group of units ⋮ On units of twisted group algebras ⋮ Identities on units of algebraic algebras

Cites Work

• PI-algebras. An introduction
• Symmetric units and group identities
• Group identities on units of rings
• Nonmatrix varieties and nil-generated algebras whose units satisfy a group identity
• Free Subgroups of Units in Group Rings
• A note on u.p. groups
• Observations on 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
• Group algebras whose units satisfy a group identity. II
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