  Let $G$ be an abstract Kac-Moody group over a finite field and $\bar{G}$ be
the closure of the image of $G$ in the automorphism group of its positive
building. We show that if the Dynkin diagram associated to $G$ is irreducible
and neither of spherical nor of affine type, then the contraction groups of
elements in $\bar{G}$ which are not topologically periodic are not closed. (In
those groups there always exist elements which are not topologically periodic.)

Group Theory