Vol. 10, No. 1, 2009

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Automorphisms of non-spherical buildings have unbounded displacement

Peter Abramenko and Ken S. Brown

Vol. 10 (2009), No. 1, 1–13

If ϕ is a nontrivial automorphism of a thick building Δ of purely infinite type, we prove that there is no bound on the distance that ϕ moves a chamber. This has the following group-theoretic consequence: If G is a group of automorphisms of Δ with bounded quotient, then the center of G is trivial.

building, automorphism, displacement, center
Mathematical Subject Classification 2000
Primary: 20E42, 51E24
Received: 5 October 2007
Accepted: 20 February 2008
Peter Abramenko
Ken S. Brown