An application of Burnside rings in elementary finite group theory
type: Item
instance of: scholarly article
title: An application of Burnside rings in elementary finite group theory
zbMATH Open document ID: 0752.19001
DOI: 10.1016/0001-8708(92)90008-9
author: Christian Siebeneicher
author: Tomoyuki Yoshida
author: Andreas W. M. Dress
published in: Advances in Mathematics
publication date: 1992-09-27T00:00:00Z
review text: Let \(C\) be a finite cyclic group and \(G\) a finite group of the same order. The authors exhibit a canonical map (called the Frobenius-Wielandt homomorphism) from the Burnside ring \(\Omega(C)\) of \(C\) into the Burnside ring \(\Omega(G)\). Then many results from elementary finite group theory are simple consequences of the existence of this map [cf. \textit{B. Huppert}, Endliche Gruppen. I (1967; Zbl 0217.07201), p. 34; and \textit{B. Wagner}, Bayreuth. Math. Schr. 6, 23-32 (1980; Zbl 0452.20001)]. An extension to profinite groups is indicated.
Mathematics Subject Classification ID: 19A22
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20E18
Mathematics Subject Classification ID: 20C15
zbMATH DE Number: 57107
zbMATH Keywords: exterior power of a \(G\)-set
zbMATH Keywords: Burnside ring
zbMATH Keywords: profinite groups
reviewed by: Marek Golasiński
MaRDI profile type: Publication
full work available at URL: 0001-8708(92)90008-9
OpenAlex ID: W1987151965
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description: scientific article; zbMATH DE number 57107