Species isomorphisms of fibered Burnside rings

Abstract

In this note, we present a notion of species isomorphism for fibered Burnside rings. We prove that a species isomorphism can be restricted to an isomorphism of mark tables, that it can be extended to an isomorphism between the ghost rings and we provide three additional characterizations of this concept. We provide an example of two non-isomorphic groups having isomorphic fibered Burnside rings for fibers in a wide family of abelian groups.