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In this note, I propose the following conjecture~: a finite group G is nilpotent if and only if its largest quotient B-group \beta(G) is nilpotent. I give a proof of...

Let G be a finite group and let k be a field. Our purpose is to investigate the simple modules for the double Burnside ring kB(G,G). It turns out that they are...

In this note I describe the structure of the biset functor $B^\times$ sending a $p$-group $P$ to the group of units of its Burnside ring $B(P)$. In particular, I show...