2003/11/26 by Martin Kassabov · 1 citation
Mathematics · #math.GR #msc:20E36 #msc:20E18 #msc:20E28
published as Ph.D. Thesis Yale University, 2003
arxiv created 2003/11/26 · arxiv updated 2009/12/01
In this thesis I study the automorphism tower of free nilpotent groups. Our main tool in studying the automorphism tower is to embed every group as a lattice in some Lie group. Using known rigidity results the automorphism group of the discrete group can be embedded into the automorphism group of the Lie group. This allows me to lift the description of the derivation tower of the free nilpotent Lie algebra to obtain information about the automorphism tower of the free nilpotent group. The main result in this thesis states that the automorphism tower of the free nilpotent group Γ(n,d) on n generators and nilpotency class d, stabilizes after finitely many steps. If the nilpotency class is small compared to the number of generators we have that the height of the automorphism tower is at most 3.