On the unit groups of partial Burnside rings

TL;DR

This paper extends the theory of partial Burnside rings by generalizing Matsuda's theorem, establishing isomorphisms between rings of different groups, and exploring the relationships involving Frobenius-Wielandt homomorphisms.

Contribution

It introduces new isomorphism results for partial Burnside rings and generalizes existing theorems, enhancing understanding of their structure and relationships.

Findings

Generalized Matsuda's theorem for partial Burnside rings

Isomorphism between partial Burnside rings of different groups

Analysis of Frobenius-Wielandt homomorphism's image in relation to group structure

Abstract

We describe the generalized Matsuda's theorem, and some results of a Burnside ring extend a partial Burnside ring. In particular, we give isomorphism between partial Burnside rings of different groups. Moreover, we consider the relationship between image of Frobenius-Wielandt homomorphism, a partial Burnside ring, and structure of a group.