Title : Locally pro-p contraction groups are nilpotent
Abstract :
A contraction group is a pair (G,t), where G is a locally compact group and t is an automorphism of G such that t^n(g)-> e as n->\infty for all g in G. It follows from results in H. Glöckner and G. A. Willis, J. Reine Angew. Math., 634 (2010), 141-169 that, if G is a totally disconnected contraction group and is locally pro-p, then it is the direct product of a p-adic Lie group and a torsion group having a composition series in which each composition factor is isomorphic to the additive group of F_p((t)). It has long been known that p-adic Lie contraction groups are nilpotent.
These ideas and results will be reviewed in the talk. Then a proof will be sketched that the torsion factor is nilpotent too. It follows, therefore, that every locally pro-p contraction group is nilpotent. This is joint work with H. Glöckner.
Timothée Marquis