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...
שמור ב:
| מחבר ראשי: | |
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| פורמט: | Livre numérique |
| שפה: | Anglais |
| יצא לאור: |
London :
Springer London
[20..].
Cham : Springer Nature |
| מהדורה: | 1st ed. 2010. |
| סדרה: | Algebra and Applications
12 |
| גישה מקוונת: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| הערה: |
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 |
| סיכום: | 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. |
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| תאור פריט: | Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| ISBN: | 9781849965040 |
| ISSN: | 2192-2950 |
| גישה: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |