The symmetry of the modular Burnside ring
Let \(k\) be a field of characteristic \(p>0\), \(G\) be a finite group, \(b(G)\) be the Burnside ring of \(G\) and let \(B_k(G)=k\otimes_\mathbb{Z} b(G)\). The blocks of \(B_k(G)\) are parametrized by the conjugacy classes of subgroups \(H\) of \(G\) satisfying \(O^p(H)=H\). The author proves that the block \(B_H\) of \(B_k(G)\) is a symmetric \(k\)-algebra if and only if \(|N_G(H):H|\) is not divisible by \(p^2\).
scientific article; zbMATH DE number 1471818