Centralizers in $\widetilde A_2$ groups

Let $Γ$ be a torsion free discrete group acting cocompactly on a two dimensional euclidean building $Δ$. The centralizer of an element of $Γ$ is either a Bieberbach group or is described by a finite graph of finite cyclic groups. Explicit examples are computed, with $Δ$ of type $\widetilde A_2$.

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