An application of Burnside rings in elementary finite group theory
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.
scientific article; zbMATH DE number 57107
scientific article