Über \(\lambda\)-Ringstrukturen auf dem Burnside-Ring
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.
scientific article; zbMATH DE number 3884361