  The authors have shown previously that every locally pro-p contraction group
decomposes into the direct product of a p-adic analytic factor and a torsion
factor. It has long been known that p-adic analytic contraction groups are
nilpotent. We show here that the torsion factor is nilpotent too, and hence
that every locally pro-p contraction group is nilpotent.

Group Theory