Academic Journal
Über \(\lambda\)-Ringstrukturen auf dem Burnside-Ring
| Τίτλος: | Über \(\lambda\)-Ringstrukturen auf dem Burnside-Ring |
|---|---|
| Συγγραφείς: | tom Dieck, Tammo |
| Στοιχεία εκδότη: | Springer, Berlin/Heidelberg |
| Θεματικοί όροι: | Ordinary representations and characters, integer valued functions, Finite nilpotent groups, \(p\)-groups, Burnside ring, Finite transformation groups, \(K\)-theory operations and generalized cohomology operations in algebraic topology, special \(\lambda \) -ring, p-group, \(\psi \) -structure, conjugacy classes |
| Περιγραφή: | The author proves: For a \(\psi^ p\)-group G the \(\psi\)-structure on the Burnside ring A(G) of G, which is defined below, induces \(\lambda^ i\)- operators that make A(G) a special \(\lambda\)-ring. Here the \(\psi^ p\)- group G is a p-group satisfying: \(H(1)=\{g^ p:\) \(g\in H\}\) as well as \(H(-1)=\{g:\) \(g^ p\in H\}\) are subgroups of G for every \(H\leq G\). Considering A(G) as part of the ring of all integer valued functions f on the conjugacy classes (H) of subgroups H of G, one defines the \(\psi\)- structure by \(\psi^ pf(H)=f(H(1))\), \(\psi^ kf=f\), when \(p\dag k\), and \(\psi^ k\psi^{\ell}=\psi^{k\ell}\). The proof has very nice identities of (p-adic) power series. |
| Τύπος εγγράφου: | Article |
| Περιγραφή αρχείου: | application/xml |
| DOI: | 10.1007/bf01174185 |
| Σύνδεσμος πρόσβασης: | https://zbmath.org/3884361 |
| Αριθμός Καταχώρησης: | edsair.c2b0b933574d..40f5b4979c0a15ac66f7204217c906f7 |
| Βάση Δεδομένων: | OpenAIRE |
| FullText | Text: Availability: 0 |
|---|---|
| Header | DbId: edsair DbLabel: OpenAIRE An: edsair.c2b0b933574d..40f5b4979c0a15ac66f7204217c906f7 RelevancyScore: 685 AccessLevel: 3 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 685 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Über \(\lambda\)-Ringstrukturen auf dem Burnside-Ring – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22tom+Dieck%2C+Tammo%22">tom Dieck, Tammo</searchLink> – Name: Publisher Label: Publisher Information Group: PubInfo Data: Springer, Berlin/Heidelberg – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Ordinary+representations+and+characters%22">Ordinary representations and characters</searchLink><br /><searchLink fieldCode="DE" term="%22integer+valued+functions%22">integer valued functions</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+nilpotent+groups%2C+%5C%28p%5C%29-groups%22">Finite nilpotent groups, \(p\)-groups</searchLink><br /><searchLink fieldCode="DE" term="%22Burnside+ring%22">Burnside ring</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+transformation+groups%22">Finite transformation groups</searchLink><br /><searchLink fieldCode="DE" term="%22%5C%28K%5C%29-theory+operations+and+generalized+cohomology+operations+in+algebraic+topology%22">\(K\)-theory operations and generalized cohomology operations in algebraic topology</searchLink><br /><searchLink fieldCode="DE" term="%22special+%5C%28%5Clambda+%5C%29+-ring%22">special \(\lambda \) -ring</searchLink><br /><searchLink fieldCode="DE" term="%22p-group%22">p-group</searchLink><br /><searchLink fieldCode="DE" term="%22%5C%28%5Cpsi+%5C%29+-structure%22">\(\psi \) -structure</searchLink><br /><searchLink fieldCode="DE" term="%22conjugacy+classes%22">conjugacy classes</searchLink> – Name: Abstract Label: Description Group: Ab Data: The author proves: For a \(\psi^ p\)-group G the \(\psi\)-structure on the Burnside ring A(G) of G, which is defined below, induces \(\lambda^ i\)- operators that make A(G) a special \(\lambda\)-ring. Here the \(\psi^ p\)- group G is a p-group satisfying: \(H(1)=\{g^ p:\) \(g\in H\}\) as well as \(H(-1)=\{g:\) \(g^ p\in H\}\) are subgroups of G for every \(H\leq G\). Considering A(G) as part of the ring of all integer valued functions f on the conjugacy classes (H) of subgroups H of G, one defines the \(\psi\)- structure by \(\psi^ pf(H)=f(H(1))\), \(\psi^ kf=f\), when \(p\dag k\), and \(\psi^ k\psi^{\ell}=\psi^{k\ell}\). The proof has very nice identities of (p-adic) power series. – Name: TypeDocument Label: Document Type Group: TypDoc Data: Article – Name: Format Label: File Description Group: SrcInfo Data: application/xml – Name: DOI Label: DOI Group: ID Data: 10.1007/bf01174185 – Name: URL Label: Access URL Group: URL Data: <link linkTarget="URL" linkTerm="https://zbmath.org/3884361" linkWindow="_blank">https://zbmath.org/3884361</link> – Name: AN Label: Accession Number Group: ID Data: edsair.c2b0b933574d..40f5b4979c0a15ac66f7204217c906f7 |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsair&AN=edsair.c2b0b933574d..40f5b4979c0a15ac66f7204217c906f7 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/bf01174185 Languages: – Text: Undetermined Subjects: – SubjectFull: Ordinary representations and characters Type: general – SubjectFull: integer valued functions Type: general – SubjectFull: Finite nilpotent groups, \(p\)-groups Type: general – SubjectFull: Burnside ring Type: general – SubjectFull: Finite transformation groups Type: general – SubjectFull: \(K\)-theory operations and generalized cohomology operations in algebraic topology Type: general – SubjectFull: special \(\lambda \) -ring Type: general – SubjectFull: p-group Type: general – SubjectFull: \(\psi \) -structure Type: general – SubjectFull: conjugacy classes Type: general Titles: – TitleFull: Über \(\lambda\)-Ringstrukturen auf dem Burnside-Ring Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: tom Dieck, Tammo IsPartOfRelationships: – BibEntity: Identifiers: – Type: issn-locals Value: edsair |
| ResultId | 1 |