  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 this conjecture under the additional assumption that G be
solvable. I also show that this conjecture is equivalent to the following: the
kernel of restrictions to nilpotent subgroups is a biset-subfunctor of the
Burnside functor.
