Locally pro-p contraction groups are nilpotent

TL;DR

This paper proves that all locally pro-p contraction groups are nilpotent by demonstrating that both their p-adic analytic and torsion components possess this property.

Contribution

It establishes the nilpotency of the torsion factor in locally pro-p contraction groups, completing the understanding of their structure.

Findings

Locally pro-p contraction groups decompose into p-adic analytic and torsion factors.

p-adic analytic contraction groups are known to be nilpotent.

The torsion factor in these groups is also shown to be nilpotent.

Abstract

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.