The Symmetry of the Modular Burnside Ring

Let b(G) be the Burnside ring of a finite group G and let k be a field of prime characteristic. It is the purpose of this paper to give a characterization of whether a block of k b(G) is a symmetric k-algebra. This proves a blockwise version of a corresponding result about k b(G) by W. Gustafson (1977, Comm. Algebra5, 1–15).