Species isomorphisms of fibered Burnside rings

TL;DR

This paper introduces the concept of species isomorphism for fibered Burnside rings, demonstrating its relation to mark tables and ghost rings, and providing multiple characterizations of this notion.

Contribution

It defines species isomorphism for fibered Burnside rings and explores its properties and characterizations, extending understanding of their algebraic structure.

Findings

Species isomorphism can be restricted to mark table isomorphisms.

It can be extended to isomorphisms between ghost rings.

Three additional characterizations of species isomorphism are provided.

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.