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Let G be a finite group. We show that the Bass Nil-groups , $n \in Z$, are generated from the p-subgroups of G by induction maps, certain twisting maps depending on elements in the centralizers of the p-subgroups, and the Verschiebung homomorphisms. As a consequence, the groups are generated by induction from elementary subgroups. For we get an improved estimate of the torsion exponent.

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