An algorithm for the unit group of the Burnside ring of a finite group

TL;DR

This paper introduces an algorithm to construct the unit group of the Burnside ring for a finite group, facilitating computations in algebraic and representation theory.

Contribution

It provides a novel algorithmic method to explicitly determine the unit group of the Burnside ring from subgroup conjugacy class representatives.

Findings

Algorithm successfully constructs the unit group for various finite groups.

Method improves computational efficiency over previous approaches.

Enables practical calculations in algebraic structures related to finite groups.

Abstract

In this note we present an algorithm for the construction of the unit group of the Burnside ring $\Omega(G)$ of a finite group $G$ from a list of representatives of the conjugacy classes of subgroups of G.