Group Identities on Units and Symmetric Units of Group Rings [recurso electrónico] / by Gregory T. Lee.

Por: Lee, Gregory T [author.]Colaborador(es): SpringerLink (Online service)Tipo de material: Texto

TextoSeries Algebra and Applications ; 12Editor: London : Springer London, 2010Descripción: XII, 196 p. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9781849965040Tema(s): Mathematics | Algebra | Group theory | Mathematics | Associative Rings and Algebras | Group Theory and GeneralizationsFormatos físicos adicionales: Printed edition:: Sin títuloClasificación CDD: 512.46 Clasificación LoC:QA251.5Recursos en línea: Libro electrónico Texto

Contenidos:

Group Identities on Units of Group Rings -- Group Identities on Symmetric Units -- Lie Identities on Symmetric Elements -- Nilpotence of and.

En: Springer eBooksResumen: Let FG be the group ring of a group G over a field F. Write U(FG) for the group of units of FG. It is an important problem to determine the conditions under which U(FG) satisfies a group identity. In the mid 1990s, a conjecture of Hartley was verified, namely, if U(FG) satisfies a group identity, and G is torsion, then FG satisfies a polynomial identity. Necessary and sufficient conditions for U(FG) to satisfy a group identity soon followed. Since the late 1990s, many papers have been devoted to the study of the symmetric units; that is, those units u satisfying u* = u, where * is the involution on FG defined by sending each element of G to its inverse. The conditions under which these symmetric units satisfy a group identity have now been determined. This book presents these results for arbitrary group identities, as well as the conditions under which the unit group or the set of symmetric units satisfies several particular group identities of interest.

Existencias ( 1 )
Notas de título ( 3 )

Existencias
Tipo de ítem	Biblioteca actual	Colección	Signatura	Copia número	Estado	Fecha de vencimiento	Código de barras
Libro Electrónico	Biblioteca Electrónica	Colección de Libros Electrónicos	QA251.5 (Browse shelf(Abre debajo))	1	No para préstamo		372939-2001

Group Identities on Units of Group Rings -- Group Identities on Symmetric Units -- Lie Identities on Symmetric Elements -- Nilpotence of and.

Let FG be the group ring of a group G over a field F. Write U(FG) for the group of units of FG. It is an important problem to determine the conditions under which U(FG) satisfies a group identity. In the mid 1990s, a conjecture of Hartley was verified, namely, if U(FG) satisfies a group identity, and G is torsion, then FG satisfies a polynomial identity. Necessary and sufficient conditions for U(FG) to satisfy a group identity soon followed. Since the late 1990s, many papers have been devoted to the study of the symmetric units; that is, those units u satisfying u* = u, where * is the involution on FG defined by sending each element of G to its inverse. The conditions under which these symmetric units satisfy a group identity have now been determined. This book presents these results for arbitrary group identities, as well as the conditions under which the unit group or the set of symmetric units satisfies several particular group identities of interest.