Über \(\lambda\)-Ringstrukturen auf dem Burnside-Ring
type: Item
instance of: scholarly article
title: Über \(\lambda\)-Ringstrukturen auf dem Burnside-Ring
zbMATH Open document ID: 0555.20008
DOI: 10.1007/BF01174185
author: Tammo tom Dieck
published in: Mathematische Zeitschrift
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173507
review text: 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.
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 55S25
zbMATH DE Number: 3884361
zbMATH Keywords: \(\psi \) -structure
zbMATH Keywords: Burnside ring
zbMATH Keywords: special \(\lambda \) -ring
zbMATH Keywords: p-group
zbMATH Keywords: integer valued functions
zbMATH Keywords: conjugacy classes
reviewed by: Jürgen Ritter
MaRDI profile type: Publication
cites work: Natural Endomorphisms of Burnside Rings
cites work: Transformation groups and representation theory
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cites work: Q3961503
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cites work: Ein Induktionssatz für rationale Charaktere von nilpotenten Gruppen.
cites work: PERMUTATION REPRESENTATIONS OF FINITE p-GROUPS
description: scientific article; zbMATH DE number 3884361