A conjecture on B-groups |
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Authors: | Serge Bouc |
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Affiliation: | 1. CNRS-LAMFA, Université de Picardie, 33 rue St Leu, 80039, Amiens Cedex 01, France
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Abstract: | 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. |
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