Serge Bouc
Published 2012-02-28Version 1
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.
On the number of $p$-elements in a finite group
Bounding the number of p'-degrees from below
The Chebotarev invariant of a finite group: a conjecture of Kowalski and Zywina
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