The contraction subgroup for x in the locally compact group, G,
con(x)={ g ∈ G ∣ xngx−n → 1 as n → ∞ },
and the Levi subgroup is
lev(x)={ g ∈ G ∣ {xngx−n}n∈ℤ has compact closure }.
The following will be shown. Let G be a totally disconnected, locally compact group and x ∈ G. Let y ∈ lev(x). Then there are x′ ∈ G and a compact subgroup, K ≤ G such that:
–K is normalized by x′ and y,
-con(x′)=con(x) and lev(x′)=lev(x) and
-the group ⟨x′,y,K⟩ is abelian modulo K, and hence flat.
If no compact open subgroup of G normalized by x and no compact open subgroup of lev(x) normalized by y, then the flat-rank of ⟨x′,y,K⟩ is equal to 2.
This video was produced by Newcastle University, Australia, as part of the Symmetries in Newcastle seminar series.
