Rigidity theorems show cocompact lattices are the unique infinite finitely generated commensurated subgroups up to commensurability in their commensurators, including for automorphism groups of trees.
Group Theory 15 (2012), no
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Lattices determined by their commensurator
Rigidity theorems show cocompact lattices are the unique infinite finitely generated commensurated subgroups up to commensurability in their commensurators, including for automorphism groups of trees.