Group Identities on Units and Symmetric Units of Group Rings
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, an...
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| Главный автор: | |
|---|---|
| Формат: | Livre numérique |
| Язык: | Anglais |
| Опубликовано: |
London :
Springer London
[20..].
Cham : Springer Nature |
| Редактирование: | 1st ed. 2010. |
| Серии: | Algebra and Applications
12 |
| Online-ссылка: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Примечание: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Group Identities on Units and Symmetric Units of Group Rings, Texte imprimé, 9781447125891 • Group Identities on Units and Symmetric Units of Group Rings, Texte imprimé, 9781849965033 • Group Identities on Units and Symmetric Units of Group Rings, Texte imprimé, 9781849965057 |
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| 100 | 1 | |a Lee, Gregory T. | |
| 245 | 1 | 0 | |a Group Identities on Units and Symmetric Units of Group Rings |c by Gregory T. Lee. |
| 250 | |a 1st ed. 2010. | ||
| 260 | |a London : |b Springer London. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Algebra and Applications |v 12 |x 2192-2950 | |
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 505 | 1 | |a Group Identities on Units of Group Rings Group Identities on Symmetric Units Lie Identities on Symmetric Elements Nilpotence of and. | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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. | ||
| 776 | 0 | |t Group Identities on Units and Symmetric Units of Group Rings |b Texte imprimé |z 9781447125891 | |
| 776 | 0 | |t Group Identities on Units and Symmetric Units of Group Rings |b Texte imprimé |z 9781849965033 | |
| 776 | 0 | |t Group Identities on Units and Symmetric Units of Group Rings |b Texte imprimé |z 9781849965057 | |
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