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تسجيل مستخدم جديدDensity of commensurators for uniform lattices of right-angled buildings
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Let G be the automorphism group of a regular right-angled building X. The standard uniform lattice Gamma_0 in G is a canonical graph product of finite groups, which acts discretely on X with quotient a chamber. We prove that the commensurator of Gamma_0 is dense in G. This result was also obtained by Haglund. For our proof, we develop carefully a technique of unfoldings of complexes of groups. We use unfoldings to construct a sequence of uniform lattices Gamma_n in G, each commensurable to Gamma_0, and then apply the theory of group actions on complexes of groups to the sequence Gamma_n. As further applications of unfoldings, we determine exactly when the group G is nondiscrete, and we prove that G acts strongly transitively on X.
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