Abstract

In this paper, we prove that each component of the Burnside ring of a finite group is the soluble component of the Burnside ring of a Weyl subgroup of its corresponding group. We show that groups with isomorphic Burnside rings have the same sublattice of soluble normal subgroups and the same spectrum. This gives for the alternating groups, the sporadic simple groups and many series of simple groups of Lie type a positive answer to Yoshida's question when a finite group is determined by its Burnside ring up to isomorphism.