Deflation and tensor induction on the Frobenius-Wielandt morphism

TL;DR

This paper investigates the conditions under which the Frobenius-Wielandt morphism commutes with deflation and tensor induction on the Burnside ring, extending previous work on induction using biset functor techniques.

Contribution

It provides new insights into the commutativity of the Frobenius-Wielandt morphism with deflation and tensor induction, employing biset functor methods where traditional techniques fail.

Findings

Identifies conditions for commutativity with deflation

Extends understanding of Frobenius-Wielandt morphism behavior

Utilizes biset functor tools for non-induction cases

Abstract

We explore conditions for the Frobenius-Wielandt morphism to commute with the operations of deflation and tensor induction on the Burnside ring. In doing this, we review the commutativity with induction. The techniques used for induction and tensor induction no longer work for deflation, so in this case we make use of tools coming from the theory of biset functors.