turkmath.org

The simple biset functors $S_{H,W}$ over a commutative ring $F$ are parametrized by pairs $(H, W)$ of a finite group $H$ and a simple FOut(H)-module $W$. When $F$ is a field of characteristic $0$, I will describe some consequences on the structure of $G$ and $H$ of the existence of a non-split extension of $S_{G,V}$ by $S_{H,W}$. On the way, the notions of 'minimal $B$-group' and 'atoric nilpotent group' will be introduced. Finally, I will consider similar results for extensions of simple functors for groups of odd order over a field of characteristic $2$.